prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the purpose of an ICD?

Read the following text and answer briefly.

Context 1: Do you know the difference between V T  and T V?
Like any exclusive club, heart disease has its own jargon, understandable only by other members of the club, particularly by cardiac care providers  For example, I remember lying in my CCU bed (that’s the Coronary Intensive Care Unit), trying to memorize the letters LAD (that’s the Left Anterior Descending, the large coronary artery whose 99% blockage had caused my MI (myocardial infarction – in my case, the so-called ‘widowmaker’ heart attack) 
To help others needing simultaneous translation of this new lingo in your research or in your own medical records, here’s a helpful list of some of the most common acronyms/terms you’ll likely find around the cardiac ward 
NOTE from CAROLYN: This entire patient-friendly, jargon-free glossary (all 8,000 words!) is also part of my book “A Woman’s Guide to Living with Heart Disease“ (Johns Hopkins University Press, November 2017) 
AA – Anti-arrhythmic: Drugs used to treat patients who have irregular heart rhythms 
Ablation – See Cardiac Ablation 
ACE Inhibitor – Angiotension Converting Enzyme inhibitor: A drug that lowers blood pressure by interfering with the breakdown of a protein-like substance involved in regulating blood pressure 
ACS – Acute Coronary Syndrome: An emergency condition brought on by sudden reduced blood flow to the heart  The first sign of acute coronary syndrome can be sudden stopping of your heart (cardiac arrest) 
AED – Automatic External Defibrillator: A portable defibrillator for use during a cardiac emergency; it can be used on patients experiencing sudden cardiac arrest by applying a brief electroshock to the heart through electrodes placed on the chest 
AF or Afib – Atrial Fibrillation: An irregular and often rapid heart rate that can cause poor blood flow to the body  Afib symptoms include heart palpitations, shortness of breath, weakness or fainting  Episodes of atrial fibrillation can come and go, or you may have chronic atrial fibrillation 
AFL – Atrial Flutter: A type of arrhythmia where the upper chambers of the heart (the atria) beat very fast, causing the walls of the lower chambers (the ventricles) to beat inefficiently as well 
A-HCM – Apical Hypertrophic Cardiomyopathy: Also called Yamaguchi Syndrome or Yamaguchi Hypertrophy, a non-obstructive form of cardiomyopathy (a disease of the heart muscle that leads to generalized deterioration of the muscle and its pumping ability) in which a portion of the heart muscle is hypertrophied (thickened) without any obvious cause although there may be a genetic link  It was first described in individuals of Japanese descent 
AI – Aortic Insufficiency: A heart valve disease in which the aortic valve does not close tightly, leading to the backward flow of blood from the aorta (the largest blood vessel) into the left ventricle (a chamber of the heart) 
AIVR – Accelerated Idioventricular Rhythm: Ventricular rhythm whose rate is greater than 49 beats/min but less than 100 beats/min, usually benign  (Ventricles are the two main chambers of the heart, left and right) 
Angina (stable) – A condition marked by distressing symptoms typically between neck and navel that come on with exertion and go away with rest, caused by an inadequate blood supply to the heart muscle typically because of narrowed coronary arteries feeding the heart muscle  Also known as Angina Pectoris  Unstable angina (UA) occurs when fatty deposits (plaques) in a blood vessel rupture or a blood clot forms, blocking or reducing flow through a narrowed artery, suddenly and severely decreasing blood flow to the heart muscle  Unstable angina is not relieved by rest; it’s dangerous and requires emergency medical attention 
Antiplatelet drugs – Medications that block the formation of blood clots by preventing the clumping of platelets (examples: Plavix, Effient, Brillinta, Ticlid, etc)  Heart patients, especially those with implanted stents after PCI, are often prescribed dual antiplatelet therapy (DAPT) which includes one of these prescribed meds along with daily low-dose aspirin 
Aorta – The main artery of the body, carrying blood from the left side of the heart to the arteries of all limbs and organs except the lungs 
Aortic Stenosis: A disease of the heart valves in which the opening of the aortic valve is narrowed  Also called AS 
Aortic valve – One of four valves in the heart, this valve allows blood from the left ventricle to be pumped up (ejected) into the aorta, but prevents blood from returning to the heart once it’s in the aorta 
AP – Apical Pulse: A central pulse located at the apex (pointy bottom) of the heart 
Apex – the lowest (pointy) tip of the heart that points downward at the base, forming what almost looks like a rounded point 
Apical Hypertrophic Cardiomyopathy (A-HCM): Also called Yamaguchi Syndrome or Yamaguchi Hypertrophy, a non-obstructive form of cardiomyopathy (a disease of the heart muscle that leads to generalized deterioration of the muscle and its pumping ability) in which a portion of the heart muscle is hypertrophied (thickened) without any obvious cause  There may be a genetic link  It was first described in people of Japanese descent 
Arrhythmia – A condition in which the heart beats with an irregular or abnormal rhythm 
AS – Aortic Stenosis: A disease of the heart valves in which the opening of the aortic valve is narrowed 
ASD – Atrial Septal Defect: See Septal Defect 
Atrial Flutter – A heart rhythm problem (arrhythmia) originating from the right atrium, most often involving a large circuit that travels around the area of the tricuspid valve (between the right atrium and the right ventricle (this is called typical atrial flutter)  Less commonly, atrial flutter can also result from circuits in other areas of the right or left atrium that cause the heart to beat fast (called atypical atrial flutter) 
Atrial Septum, the membrane that separates the left and the right upper chambers of the heart (the atria) 
Atrium – A chamber of the heart that receives blood from the veins and forces it into a ventricle or ventricles  Plural: atria 
AV – Atrioventricular: A group of cells in the heart located between the upper two chambers (the atria) and the lower two chambers (the ventricles) that regulate the electrical current that passes through it to the ventricles  Also Atrioventricular Block: An interruption or disturbance of the electrical signal between the heart’s upper two chambers (the atria) and lower two chambers (the ventricles)  Also Aortic valve: The valve that regulates blood flow from the heart into the aorta 
AVNRT – Atrioventricular Nodal Re-entry Tachycardia: a heart rhythm problem that happens when there’s an electrical short circuit in the centre of the heart, one of the most common types of SVT, most often seen in people in their twenties and thirties, and more common in women than in men 
BAV – Bicuspid Aortic Valve: The most common malformation of the heart valves in which the aortic valve has only two cusps instead of three 
BB – Beta Blocker: A blood pressure-lowering drug that limits the activity of epinephrine, a hormone that increases blood pressure 
BBB – Bundle Branch Block: – A condition in which parts of the heart’s conduction system are defective and unable to normally conduct the electrical signal, causing an irregular heart rhythm (arrhythmia) 
BMI – Body mass index: A number that doctors use to determine if you’re overweight  BMI is calculated using a formula of weight in kilograms divided by height in meters squared (BMI =W [kg]/H [m2])  Better yet, just click here to figure out your own BMI 
BNP blood test – BNP (B-type Natriuretic Peptide) is a substance secreted from the ventricles or lower chambers of the heart in response to changes in pressure that happen when heart failure develops and/or worsens  The level of BNP in the blood increases when heart failure symptoms worsen, and decreases when the heart failure condition is stable 
BP – Blood Pressure: The force or pressure exerted by the heart in pumping blood; the pressure of blood in the arteries  See also hypertension 
BrS – Brugada Syndrome: Brugada syndrome is a genetic heart disease that is characterized by distinctively abnormal electrocardiogram (EKG/ECG) findings and an increased risk of sudden cardiac arrest 
CAA – Coronary artery anomaly: A congenital defect in one or more of the coronary arteries of the heart 
CABG – Coronary Artery Bypass Graft: A surgical procedure that reroutes blood flow around a diseased or blocked blood vessel that supplies blood to the heart by grafting either a piece of vein harvested from the leg or the artery from under the breastbone 
CA – Coronary Artery: The arteries arising from the aorta that arch down over the top of the heart and divide into branches  They provide blood to the heart muscle 
CAD – Coronary Artery Disease: A narrowing of the arteries that supply blood to the heart  The condition results from a plaque rupture/blood clot or spasm and greatly increases the risk of a heart attack 
Cardiac Ablation – A procedure performed by an Electrophysiologist (EP) – a cardiologist with specialized training in treating heart rhythm problems – that typically uses catheters — long, flexible tubes inserted through a vein in the groin and threaded to the heart — to correct structural problems in the heart that cause an arrhythmia  Cardiac ablation works by scarring or destroying the tissue in your heart that triggers an abnormal heart rhythm 
Cardiac Arrest – Also known as Sudden Cardiac Arrest: The stopping of the heartbeat, usually because of interference with the electrical signal that regulates each heartbeat (often associated with coronary heart disease)  Can lead to Sudden Cardiac Death 
Cardiac Catheterization – An invasive procedure in which a catheter is inserted through a blood vessel in the wrist/arm or groin with x-ray guidance  This procedure can help provide information about blood supply through the coronary arteries, blood pressure, blood flow throughout the chambers of the heart, collection of blood samples, and x-rays of the heart’s ventricles or arteries  It’s typically performed in the cath lab during angiography 
Cardiac Resynchronization Therapy (CRT) also called bi-ventricular pacemaker: an electronic pacing device that’s surgically implanted in the chest to treat the delay in heart ventricle contractions that occur in some people with heart failure 
Cardiac Tamponade – Pressure on the heart that occurs when blood or fluid builds up in the space between the heart muscle (myocardium) and the outer covering sac of the heart (pericardium)  Also called Tamponade 
Cardiomyopathy – a chronic disease of the heart muscle (myocardium), in which the muscle is abnormally enlarged, thickened, and/or stiffened 
Cardioversion – A medical procedure in which an abnormally fast heart rate (tachycardia) or cardiac arrhythmia like atrial fibrillation is converted to a normal rhythm using electricity or drugs  Synchronized electrical cardioversion uses a therapeutic dose of electric current to the heart at a specific moment in the cardiac cycle  Chemical cardioversion uses medications to convert to normal rhythm 
Cath lab – the room in the hospital/medical clinic where cardiac catheterization procedures take place (for example, when a stent is implanted into a blocked coronary artery) 
CCB – Calcium Channel Blocker: A drug that lowers blood pressure by regulating calcium-related electrical activity in the heart 
CDS – Cardiac Depression Scale: A scale that can help assess the effects of depression occurring as a result of a heart disease diagnosis 
CHF – Heart Failure (also called Congestive Heart Failure): A condition in which the heart cannot pump all the blood returning to it, leading to a backup of blood in the vessels and an accumulation of fluid in the body’s tissues, including the lungs 
CM – Cardiomyopathy: A disease of the heart muscle that leads to generalized deterioration of the muscle and its pumping ability 
CO – Cardiac Output: The amount of blood the heart pumps through the circulatory system in one minute 
Collateral arteries – These extra coronary blood vessels are sometimes able to bypass a blockage in an artery in order to supply enough oxygenated blood to enable the heart muscle to survive when in danger of being damaged because of blockage(s) 
Collateral arteries – Blood vessels that provide an alternative arterial supply of blood to an area of the heart that’s in danger of being deprived of oxygenated blood because of one or more blocked arteries 
Congenital heart defect – one of about 35 different types of heart conditions that happen when the heart or the blood vessels near the heart don’t develop normally before a baby is born (in about 1% of live births)  Because of medical advances that treat babies born with heart defects, there are now for the first time more adults with congenital heart disease than children 
Congestive heart failure (CHF) – a chronic progressive condition that affects the pumping power of your heart muscle  Often referred to simply as heart failure, CHF specifically refers to the stage in which fluid builds up around the heart and causes it to pump inefficiently 
COPD – Chronic Obstructive Pulmonary Disease: A lung disease defined by persistently poor airflow as a result of breakdown of lung tissue (known as emphysema) and dysfunction of the small airways Often associated with smoking, it typically worsens over time 
Coronary Microvascular Disease – A heart condition that causes impaired blood flow to the heart muscle through the small vessels of the heart  Also called Microvascular Disease or Small Vessel Disease 
Coronary Reactivity Test – An angiography procedure specifically designed to examine the blood vessels in the heart and how they respond to different medications  Physicians use these images to distinguish different types of blood vessel reactivity dysfunction (such as Coronary Microvascular Disease) 
Costochondritis– the cause of severe chest pain, but NOT heart-related; it’s an inflammation of the cartilage that connects a rib to the breastbone 
Coumadin – A drug taken to prevent the blood from clotting and to treat blood clots  Coumadin is believed to reduce the risk of blood clots causing strokes or heart attacks  See also Warfarin 
Cox Maze procedure – A complex “cut-and-sew” surgical procedure done to treat atrial fibrillation through a complicated set of incisions made in a maze-like pattern on the left and right atria (the upper chambers of the heart) to permanently interrupt the abnormal electrical signals that are causing the irregular heartbeats of Afib  See also: Mini-Maze 
CP – Chest Pain (may also be felt as squeezing, pressure, fullness, pressure, heaviness, burning or tightness in the chest) 
CPR – Cardiopulmonary Resuscitation: An emergency procedure in which the heart and lungs are made to work by manually compressing the chest overlying the heart and forcing air into the lungs, used to maintain circulation when the heart stops pumping during Cardiac Arrest  Current guidelines suggest hands-only CPR  See also AED 
CQ10 – Co-enzyme Q10: A dietary supplement sometimes recommended for heart patients taking statin drugs 
CRP – C-reactive protein: A byproduct of inflammation, produce by the liver, found in the blood in some cases of acute inflammation 
CRT – Cardiac Resynchronization Therapy also called bi-ventricular pacemaker: an electronic pacing device that’s surgically implanted in the chest to treat the delay in heart ventricle contractions that occur in some people with heart failure 
CT – Computed tomography (CT or CAT scan): An x-ray technique that uses a computer to create cross-sectional images of the body 
CTA – Computerized Tomographic Angiogram: An imaging test to look at the arteries that supply the heart muscle with blood  Unlike a traditional coronary angiogram, CT angiograms don’t use a catheter threaded through your blood vessels to your heart but instead rely on a powerful X-ray machine to produce images of your heart and heart vessels 
CV – Coronary Vein: One of the veins of the heart that drain blood from the heart’s muscular tissue and empty into the right atrium 
CV – Cardiovascular: Pertaining to the heart and blood vessels that make up the circulatory system 
DBP – Diastolic blood pressure: The lowest blood pressure measured in the arteries  It occurs when the heart muscle is relaxed between beats 
DCM – Dilated Cardiomyopathy: A disease of the heart muscle, primarily affecting the heart’s main pumping chamber (left ventricle)  The left ventricle becomes enlarged (dilated) and can’t pump blood to your body with as much force as a healthy heart can 
DDI – Drug-drug interaction: A situation in which a medication affects the activity of another medication when both are administered together 
DIL – Diltiazem: A calcium channel blocker drug that acts as a vasodilator; used in the treatment of angina pectoris, hypertension, and supraventricular tachycardia 
Diuretic – A class of drugs used to lower blood pressure  Also known as “water pills” 
Dobutamine stress echocardiography: This is a form of a stress echocardiogram diagnostic test  But instead of exercising on a treadmill or exercise bike to stress the heart, the stress is obtained by giving a drug that stimulates the heart and makes it “think” it’s exercising  The test is used to evaluate your heart and valve function if you are unable to exercise  It is also used to determine how well your heart tolerates activity, and your likelihood of having coronary artery disease (blocked arteries), and it can evaluate the effectiveness of your cardiac treatment plan  See also TTE and Stress Echocardiogram 
Dressler’s syndrome – Happens to a small number of people three to four weeks after a heart attack  The heart muscle that died during the attack sets the immune system in motion, calling on lymphocytes, one of the white blood cells, to infiltrate the coverings of the heart (pericardium) and the lungs (pleura)  It also starts generating antibodies, which attack those two coverings  Chest pain (CP) is the predominant symptom; treated with anti-inflammatory drugs 
Dual Antiplatelet Therapy – Medications that block the formation of blood clots by preventing the clumping of platelets (examples Plavix, Effient, Brillinta, Ticlid, etc ) are often prescribed along with aspirin as part of what’s known as dual antiplatelet therapy, especially to patients who have undergone PCI and stent implantation 
DVT – Deep Vein Thrombosis: A blood clot in a deep vein in the calf 
ECG / EKG – Electrocardiogram: A test in which several electronic sensors are placed on the body to monitor electrical activity associated with the heartbeat 
Ectopic beats – small changes in an otherwise normal heartbeat that lead to extra or skipped heartbeats, often occurring without a clear cause, most often harmless 
EF – Ejection Fraction: A measurement of blood that is pumped out of a filled ventricle  The normal rate is 50-60% 
EKG/ECG – Electrocardiogram: A test in which several electronic sensors are placed on the body to monitor electrical activity associated with the heartbeat 
Endothelium: A single-cell layer of flat endothelial cells lining the closed internal spaces of the body such as the inside of blood vessels  Endothelial dysfunction affects the ability of these cells to help dilate blood vessels, control inflammation or prevent blood clots  The endothelium is associated with most forms of cardiovascular disease, such as hypertension, coronary artery disease, chronic heart failure, peripheral vascular disease, diabetes, chronic kidney failure, and severe viral infections 
Enhanced External Counterpulsation – EECP is an FDA-approved non-invasive, non-drug treatment for angina  It works by promoting the development of collateral coronary arteries  The therapy is widely used in prominent heart clinics such as the Cleveland Clinic, Mayo Clinic and Johns Hopkins – especially for patients who are not good candidates for invasive procedures such as bypass surgery, angioplasty or stenting 
EP – Electrophysiologist: A cardiologist who has additional training in diagnosing/treating heart rhythm disorders 
EPS – Electrophysiology Study: A test that uses cardiac catheterization to study patients who have arrhythmias (abnormal hear rhythm)  An electrical current stimulates the heart in an effort to provoke an arrhythmia, which is immediately treated with medications  EPS is used primarily to identify the origin of the arrhythmia and to test the effectiveness of medications used to treat abnormal heart rhythms 
EVH – Endoscopic Vessel Harvesting: To create the bypass graft during CABG open heart surgery, a surgeon will remove or “harvest” healthy blood vessels from another part of the body, often from the patient’s leg or arm  This vessel becomes a graft, with one end attaching to a blood source above and the other end below the blocked area  See CABG 
Exercise stress test – An exercise test (walking/running on a treadmill or pedalling a stationary bike) to make your heart work harder and beat faster  An EKG is recorded while you exercise to monitor any abnormal changes in your heart under stress, with or without the aid of drugs to enhance this assessment  See also: MIBI, Echocardiogram, Nuclear Stress Test 
Familial hypercholesterolemia (FH) – A genetic predisposition to dangerously high cholesterol levels  FH is an inherited disorder that can lead to aggressive and premature cardiovascular disease, including problems like heart attacks, strokes, or narrowing of the heart valves 
Femoral Artery: a major artery in your groin/upper thigh area, through which a thin catheter is inserted, eventually making its way into the heart during angioplasty to implant a stent; currently the most widely used angioplasty approach in the United States, but many other countries now prefer the Radial Artery access in the wrist 
FFR – Fractional Flow Reserve: A test used during coronary catheterization (angiogram) to measure pressure differences across a coronary artery stenosis (narrowing or blockage) defined as as the pressure behind a blockage relative to the pressure before the blockage 
HC – High Cholesterol: When fatty deposits build up in your coronary arteries 
HCTZ – Hydrochlorothiazide: A drug used to lower blood pressure; it acts by inhibiting the kidneys’ ability to retain water  Used to be called “water pills” 
Heart Failure – a chronic progressive condition that affects the pumping power of your heart muscle  Sometimes called Congestive Heart Failure (CHF) 
Holter Monitor – A portable monitoring device that patients wear for recording heartbeats over a period of 24 hours or more 
HTN – Hypertension: High blood pressure, the force of blood pushing against the walls of arteries as it flows through them 
Hypokinesia – Decreased heart wall motion during each heartbeat, associated with cardiomyopathy, heart failure, or heart attack  Hypokinesia can involve small areas of the heart (segmental) or entire sections of heart muscle (global)  Also called hypokinesis 
ICD – Implantable Cardioverter Defibrillator: A surgically implanted electronic device to treat life-threatening heartbeat irregularities 
IHD – Ischemic Heart Disease: heart problems caused by narrowing of the coronary arteries, causing a decreased blood supply to the heart muscle  Also called coronary artery disease and coronary heart disease 
INR – International Normalized Ratio: A laboratory test measure of blood coagulation, often used as a standard for monitoring the effects of the anti-coagulant drug, warfarin (coumadin) 
IST – Inappropriate sinus tachycardia: A heart condition seen most often in young women, in which a person’s resting heart rate is abnormally high (greater than 100 bpm), their heart rate increases rapidly with minimal exertion, and this rapid heart rate is accompanied by symptoms of palpitations, fatigue, and/or exercise intolerance 
Interventional cardiologist – A cardiologist who is trained to perform invasive heart procedures like angiography, angioplasty, percutaneous coronary intervention (PCI), implanting stents, etc 
IVS – Interventricular Septum: The stout wall that separates the lower chambers (the ventricles) of the heart from one another 
IVUS – Intravascular Ultrasound: A form of echocardiography performed during cardiac catheterization in which a transducer (a device that can act as a transmitter (sender) and receiver of ultrasound information) is threaded into the heart blood vessels via a catheter; it’s used to provide detailed information about the blockage inside the blood vessels 
LAD – Left Anterior Descending coronary artery: One of the heart’s coronary artery branches from the left main coronary artery which supplies blood to the left ventricle 
LAFB – Left Anterior Fascicular Block: A cardiac condition,distinguished from Left Bundle Branch Block because only the anterior half of the left bundle branch is defective and more common than left posterior fascicular block 
LAHB – Left Anterior Hemiblock: The Left Bundle Branch divides into two major branches – the anterior and the posterior fascicles  Occasionally, a block can occur in one of these fascicles 
Left Circumflex Artery – The artery carries oxygenated blood from the heart to the body; it’s a branch of the Left Main Coronary Artery after the latter runs its course in between the aorta and the Main Pulmonary Artery 
Left Main Coronary Artery – The artery that branches from the aorta to supply oxygenated blood to the heart via the Left Anterior Descending Artery (LAD) and the Left Circumflex Artery 
Lipids – fat-like substances found in your blood and body tissues; a lipid panel is a blood test that measures the level of specific lipids in blood to help assess your risk of cardiovascular disease, measuring four types of lipids: total cholesterol, HDL cholesterol, LDL cholesterol, and triglycerides 
Lipoprotein-a or Lp(a) – molecules made of proteins and fat, carrying cholesterol and similar substances through the blood  A high level of Lp(a) is considered a risk factor for heart disease; detectable via a blood test 
Long QT syndrome (LQTS): A heart rhythm disorder that can potentially cause fast, chaotic heartbeats that may trigger a sudden fainting spell or seizure  In some cases, the heart may beat erratically for so long that it can cause sudden death 
LV – Left Ventricle – One of four chambers (two atria and two ventricles) in the human heart, it receives oxygenated blood from the left atrium via the mitral valve, and pumps it into the aorta via the aortic valve 
LVAD – Left ventricular assist device: A mechanical device that can be placed outside the body or implanted inside the body  An LVAD does not replace the heart – it “assists” or “helps” it pump oxygen-rich blood from the left ventricle to the rest of the body, usually as a bridge to heart transplant 
LVH – Left Ventricular Hypertrophy: A thickening of the myocardium (muscle) of the Left Ventricle (LV) of the heart  
Lumen – The hollow area within a tube, such as a blood vessel 
Main Pulmonary Artery – Carries oxygen-depleted blood from the heart to the lungs 
MIBI – Nuclear Stress Test/Cardiac Perfusion Scan/Sestamibi: tests that are used to assess the blood flow to the heart muscle (myocardium) when it is stressed by exercise or medication, and to find out what areas of the myocardium have decreased blood flow due to coronary artery disease  This is done by injecting a tiny amount of radionuclide like thallium or technetium (chemicals which release a type of radioactivity called gamma rays) into a vein in the arm or hand 
Microvascular disease – a heart condition that causes impaired blood flow to the heart muscle through the small blood vessels of the heart  Symptoms mimic those of a heart attack  Also called Coronary Microvascular Disease or Small Vessel Disease  I live with this diagnosis and have written more about it here, here and here 
Mini-Maze – a surgical procedure to treat atrial fibrillation, less invasive than what’s called the Cox Maze III procedure (a “cut-and-sew” procedure), and performed on a beating heart without opening the chest 
Mitral Valve: One of four valves in the heart, the structure that controls blood flow between the heart’s left atrium (upper chamber) and left ventricle (lower chamber)  The mitral valve has two flaps (cusps)  See also MV and/or Valves 
Mitral valve prolapse: a condition in which the two valve flaps of the mitral valve don’t close smoothly or evenly, but instead bulge (prolapse) upward into the left atrium; also known as click-murmur syndrome, Barlow’s syndrome or floppy valve syndrome 
MR – Mitral regurgitation: (also mitral insufficiency or mitral incompetence) a heart condition in which the mitral valve does not close properly when the heart pumps out blood  It’s the abnormal leaking of blood from the left ventricle, through the mitral valve and into the left atrium when the left ventricle contracts 
MRI – Magnetic Resonance Imaging: A technique that produces images of the heart and other body structures by measuring the response of certain elements (such as hydrogen) in the body to a magnetic field  An MRI can produce detailed pictures of the heart and its various structures without the need to inject a dye 
MS – Mitral Stenosis: A narrowing of the mitral valve, which controls blood flow from the heart’s upper left chamber (the left atrium) to its lower left chamber (the left ventricle)  May result from an inherited (congenital) problem or from rheumatic fever 
MUGA – Multiple-Gated Acquisition Scanning: A non-invasive nuclear test that uses a radioactive isotope called technetium to evaluate the functioning of the heart’s ventricles 
Murmur – Noises superimposed on normal heart sounds  They are caused by congenital defects or damaged heart valves that do not close properly and allow blood to leak back into the originating chamber 
MV – Mitral Valve: The structure that controls blood flow between the heart’s left atrium (upper chamber) and left ventricle (lower chamber) 
Myocardial Infarction (MI, heart attack) – The damage or death of an area of the heart muscle (myocardium) resulting from a blocked blood supply to the area  The affected tissue dies, injuring the heart 
Myocardium – The muscular tissue of the heart 
New Wall-Motion Abnormalities – Results seen on an echocardiogram test report (see NWMA, below) 
Nitroglycerin – A medicine that helps relax and dilate arteries; often used to treat cardiac chest pain (angina)  Also called NTG or GTN 
NSR – Normal Sinus Rhythm: The characteristic rhythm of the healthy human heart  NSR is considered to be present if the heart rate is in the normal range, the P waves are normal on the EKG/ECG, and the rate does not vary significantly 
NSTEMI – Non-ST-segment-elevation myocardial infarction: The milder form of the two main types of heart attack  An NSTEMI heart attack does not produce an ST-segment elevation seen on an electrocardiogram test (EKG)  See also STEMI 
Nuclear Stress Test – A diagnostic test that usually involves two exercise stress tests, one while you’re exercising on a treadmill/stationary bike or with medication that stresses your heart, and another set while you’re at rest  A nuclear stress test is used to gather information about how well your heart works during physical activity and at rest  See also: Exercise stress test, Nuclear perfusion test, MIBI 
Open heart surgery – Any surgery in which the chest is opened and surgery is done on the heart muscle, valves, coronary arteries, or other parts of the heart (such as the aorta)  See also CABG 
Pacemaker – A surgically implanted electronic device that helps regulate the heartbeat 
PAD – Peripheral Artery Disease: A common circulatory problem in which narrowed arteries reduce blood flow to the limbs, usually to the legs  Symptoms include leg pain when walking (called intermittent claudication) 
PAF – Paroxysmal Atrial Fibrillation: Atrial fibrillation that lasts from a few seconds to days, then stops on its own  See also Atrial Fibrillation 
Palpitations – A noticeably rapid, strong, or irregular heartbeat due to agitation, exertion or illness 
Paroxysmal Atrial Fibrillation – An unusual heart arrhythmia of unknown origin, at one time believed to be associated with an unusual sensitivity to alcohol consumption 
PDA – patent ductus arteriosus: A persistent opening between two major blood vessels leading from the heart  The opening is called ductus arteriosus and is a normal part of a baby’s circulatory system before birth that usually closes shortly after birth  But when it remains open, it’s called a patent ductus arteriosus  If it’s small, it may never need treatment, but a large PDA left untreated can allow poorly oxygenated blood to flow in the wrong direction, weakening the heart muscle and causing heart failure or other complications 
Pericardium: two thin layers of a sac-like tissue that surround the heart, hold it in place and help it work 
PET – Positron Emission Tomography: A non-invasive scanning technique that uses small amounts of radioactive positrons (positively charged particles) to visualize body function and metabolism  In cardiology, PET scans are used to evaluate heart muscle function in patients with coronary artery disease or cardiomyopathy 
PFO – Patent Forman Ovale: An opening between the left and right atria (the upper chambers) of the heart  Everyone has a PFO before birth, but in 1 out of every 3 or 4 people, the opening does not close naturally as it should after birth 
Plaque – A deposit of fatty (and other) substances in the inner lining of the artery wall; it is characteristic of atherosclerosis 
POTS – Postural Orthostatic Tachycardia Syndrome: A disorder that causes an increased heart rate when a person stands upright 
PPCM – Post-partum cardiomyopathy: A form of cardiomyopathy that causes heart failure toward the end of pregnancy or in the months after delivery, in the absence of any other cause of heart failure 
Preeclampsia – a late-pregnancy complication identified by spikes in blood pressure, protein in the urine, possible vision problems  Women who experience pregnancy complications like preeclampsia are at significantly higher risk for heart disease 
Prinzmetal’s Variant Angina – Chest pain caused by a spasm in a coronary artery that supplies blood to the heart muscle 
PSVT – Paroxysmal Supraventricular Tachycardia: – An occasional rapid heart rate (150-250 beats per minute) that is caused by events triggered in areas above the heart’s lower chambers (the ventricles)  “Paroxysmal” means from time to time  See also supraventricular tachycardia (SVT) 
Pulmonary Valve: One of the four valves in the heart, located between the pulmonary artery and the right ventricle of the heart, moves blood toward the lungs and keeps it from sloshing back into the heart 
PV – Pulmonary Vein: A vein carrying oxygenated blood from the lungs to the left atrium of the heart 
PVC – Premature Ventricular Contraction: An early or extra heartbeat that happens when the heart’s lower chambers (the ventricles) contract too soon, out of sequence with the normal heartbeat  In the absence of any underlying heart disease, PVCs do not generally indicate a problem with electrical stability, and are usually benign 
RA – Right Atrium: The right upper chamber of the heart  The right atrium receives de-oxygenated blood from the body through the vena cava and pumps it into the right ventricle which then sends it to the lungs to be oxygenated 
Radial Artery: the artery in the wrist where a thin catheter is inserted through the body’s network of arteries in the arm and eventually into the heart during a procedure to implant a stent  Doctors may also call this transradial access, the transradial approach, or transradial angioplasty  Because it’s associated with fewer complications, this is increasingly considered the default access approach in most countries, except in the U S  where the traditional Femoral Artery (groin) approach is still the most popular access 
RBBB – Right Bundle Branch Block: A delay or obstruction along the pathway that electrical impulses travel to make your heart beat  The delay or blockage occurs on the pathway that sends electrical impulses to the right side of your heart  See also Left Bundle Branch Block 
RCA – Right Coronary Artery: An artery that supplies blood to the right side of the heart 
Restenosis – The re-closing or re-narrowing of an artery after an interventional procedure such as angioplasty or stent placement  Sometimes called “stent failure” 
RHD – Rheumatic Heart Disease: Permanent damage to the valves of the heart caused especially by repeated attacks of rheumatic fever 
RM – Right Main coronary artery: A blood vessel that supplies oxygenated blood to the walls of the heart’s ventricles and the right atrium 
RV – Right Ventricle: The lower right chamber of the heart that receives de-oxygenated blood from the right atrium and pumps it under low pressure into the lungs via the pulmonary artery 
SA – Sinus node: The “natural” pacemaker of the heart  The node is a group of specialized cells in the top of the right atrium which produces the electrical impulses that travel down to eventually reach the ventricular muscle, causing the heart to contract 
SB – Sinus Bradycardia: Abnormally slow heartbeat 
SBP – Systolic Blood Pressure: The highest blood pressure measured in the arteries  It occurs when the heart contracts with each heartbeat  Example: the first number in 120/80 
SCAD – Spontaneous Coronary Artery Dissection: A rare emergency condition that occurs when a tear forms in one of the blood vessels in the heart, causing a heart attack, abnormalities in heart rhythm and/or sudden death  SCAD tends to strike young healthy women with few if any cardiac risk factors 
SD – Septal defect: A hole in the wall of the heart separating the atria (two upper chambers of the heart) or in the wall of the heart separating the ventricles (two lower chambers) 
Sestamibi stress test – See MIBI 
Short QT intervals (SQT): An abnormal heart rhythm where the heart muscle takes a shorter time to recharge between beats  It can cause a variety of complications from fainting and dizziness to sudden cardiac arrest 
Sick Sinus Syndrome (also known as sinus node dysfunction) is caused by an electrical problem in the heart; a group of related heart conditions that can affect how the heart beats, most commonly in older adults, although it can be diagnosed in people of any age  “Sick sinus” refers to the sinoatrial node (see below)  In people with sick sinus syndrome, the SA node does not function normally 
Sinoatrial node (SA): also commonly called the sinus node; it’s a small bundle of neurons situated in the upper part of the wall of the right atrium (the right upper chamber of the heart)  The heart’s electrical impulses are generated there  It’s the normal natural pacemaker of the heart and is responsible for the initiation of each heartbeat 
Spontaneous Coronary Artery Dissection (SCAD) – A rare emergency condition that occurs when a tear forms in one of the blood vessels in the heart, causing a heart attack, abnormalities in heart rhythm and/or sudden death  SCAD tends to strike young healthy women with few if any cardiac risk factors 
SSS – Sick Sinus Syndrome: The failure of the sinus node to regulate the heart’s rhythm 
ST – Sinus Tachycardia: A heart rhythm with elevated rate of impulses originating from the sinoatrial node, defined as greater than 100 beats per minute (bpm) in an average adult  The normal heart rate in the average adult ranges from 60–100 bpm  Also called sinus tach or sinus tachy 
Statins – Any of a class of drugs that lower the levels of low-density lipoproteins (LDL) – the ‘bad’ cholesterol in the blood – by inhibiting the activity of an enzyme involved in the production of cholesterol in the liver  Examples of brand name statins: Lipitor, Crestor, Zocor, Mevacor, Levachol, Lescol, etc  Also available as a cheaper generic form of the drug 
STEMI – ST-elevation heart attack (myocardial infarction)  The more severe form of the two main types of heart attack  A STEMI produces a characteristic elevation in the ST segment on an electrocardiogram (EKG)  The elevated ST segment is how this type of heart attack got its name  See also NSTEMI 
Stent – An implantable device made of expandable, metal mesh (looks a bit like a tiny chicken wire tube) that is placed (by using a balloon catheter) at the site of a narrowing coronary artery during an angioplasty procedure  The stent is then expanded when the balloon fills, the balloon is removed, and the stent is left in place to help keep the artery open  TRIVIA ALERT: the coronary stent was named after Charles Stent (1807-1885), an English dentist who invented a compound to produce dentures and other things like skin grafts and hollow tubes (essentially what a metal coronary stent is)  His real claim to fame occurred when he suggested using his material to coat underwater trans-Atlantic cable, which had broken several times as a result of corrosion by seawater  You’re welcome 
Stint – a common spelling mistake when what you really mean is the word “stent” (see above) 
Stress Echocardiography – A standard echocardiogram test that’s performed while the person exercises on a treadmill or stationary bicycle  This test can be used to visualize the motion of the heart’s walls and pumping action when the heart is stressed, possibly revealing a lack of blood flow that isn’t always apparent on other heart tests  The echocardiogram is performed just before and just after the exercise part of the procedure  See also TTE 
Sudden Cardiac Arrest – The stopping of the heartbeat, usually because of interference with the electrical signal (often associated with coronary heart disease)  Can lead to Sudden Cardiac Death 
Takotsubo Cardiomyopathy – A heart condition that can mimic a heart attack  Sometimes called Broken Heart Syndrome, it is not a heart attack, but it feels just like one, with common symptoms like severe chest pain and shortness of breath  It sometimes follows a severe emotional stress  Over 90% of reported cases are in women ages 58 to 75  Also referred to as Broken Heart Syndrome, stress cardiomyopathy, stress-induced cardiomyopathy or apical ballooning syndrome 
TAVR – Transcatheter aortic valve replacement: A minimally invasive procedure to repair a damaged or diseased aortic valve  A catheter is inserted into an artery in the groin and threaded to the heart  A balloon at the end of the catheter, with a replacement valve folded around it, delivers the new valve to take the place of the old  Also called TAVI (Transcatheter aortic valve implantation) 
Tetralogy of Fallot – A rare condition caused by a combination of four heart defects that are present at birth, affecting the structure of the heart and causing oxygen-poor blood to flow out of the heart and into the rest of the body  Infants and children with Tetralogy of Fallot usually have blue-tinged skin because their blood doesn’t carry enough oxygen  Often diagnosed in infancy, but sometimes not until later in life depending on severity 
Tg – Triglycerides: The most common fatty substance found in the blood; normally stored as an energy source in fat tissue  High triglyceride levels may thicken the blood and make a person more susceptible to clot formation  High triglyceride levels tend to accompany high cholesterol levels and other risk factors for heart disease, such as obesity 
TIA – Transient Ischemic Attack: A stroke-like event that lasts only for a short time and is caused by a temporarily blocked blood vessel 
TEE – Transesophageal echocardiogram: This test involves an ultrasound transducer inserted down the throat into the esophagus in order to take clear images of the heart structures without the interference of the lungs and chest 
Treadmill Stress Test – See Exercise Stress Test 
troponin – a type of cardiac enzyme found in heart muscle, and released into the blood when there is damage to the heart (for example, during a heart attack)  A positive blood test that shows elevated troponin is the preferred test for a suspected heart attack because it is more specific for heart injury than other blood tests, especially the newer high sensitivity troponin tests (hs-cTnT) 
TTE – Transthoracic Echocardiogram: This is the standard echocardiogram, a painless test similar to X-ray, but without the radiation, using a hand-held device called a transducer placed on the chest to transmit high frequency sound waves (ultrasound)  These sound waves bounce off the heart structures, producing images and sounds that can be used by the doctor to detect heart damage and disease 
TV – Tricuspid Valve: One of four one-way valves in the heart, a structure that controls blood flow from the heart’s upper right chamber (the right atrium) into the lower right chamber (the right ventricle) 
UA or USA – Unstable Angina: Chest pain that occurs when diseased blood vessels restrict blood flow to the heart; symptoms are not relieved by rest; considered a dangerous and emergency crisis requiring immediate medical help 
Valves: Your heart has four one-way valves that keep blood flowing in the right direction  Blood enters the heart first through the tricuspid valve, and next goes through the pulmonary valve (sometimes called the pulmonic valve) on its way to the lungs  Then the blood returning from the lungs passes through the mitral (bicuspid) valve and leaves the heart through the aortic valve 
Vasodilator: A drug that causes dilation (widening) of blood vessels 
Vasospasm: A blood vessel spasm that causes sudden constriction, reducing its diameter and blood flow to the heart muscle  See also Prinzmetal’s Variant Angina 
VB – Ventricular Bigeminy: A heart rhythm condition in which the heart experiences two beats of the pulse in rapid succession 
Vena Cava – a large vein that carryies de-oxygenated blood into the heart  There are two in humans, the inferior vena cava (carrying blood from the lower body) and the superior vena cava (carrying blood from the head, arms, and upper body) 
Ventricle – each of the two main chambers of the heart, left and right 
VF – Ventricular Fibrillation: A condition in which the ventricles (two lower chambers of the heart) contract in a rapid, unsynchronized fashion  When fibrillation occurs, the ventricles cannot pump blood throughout the body  Most sudden cardiac deaths are caused by VF or ventricular tachycardia (VT) 
VLDL – Very Low Density Lipoprotein: Molecules made up of mostly triglycerides, cholesterol and proteins  VLDL, also known as the “very bad” cholesterol, carries cholesterol from the liver to organs and tissues in the body  It may lead to low density lipoproteins (LDL), associated with higher heart disease risks  VLDL levels are tricky to measure routinely, and are usually estimated as a percentage of your triglyceride levels  By reducing triglycerides, you are usually also reducing your VLDL levels 
Warfarin – A drug taken to prevent the blood from clotting and to treat blood clots  Warfarin is believed to reduce the risk of blood clots causing strokes or heart attacks  Also known as Coumadin 
Widowmaker heart attack – The type of heart attack I survived, since you asked  A nickname doctors use to describe a severely blocked left main coronary artery or proximal left anterior descending coronary artery of the heart  This term is used because if the artery gets abruptly and completely blocked, it can cause a massive heart attack that will likely lead to sudden cardiac death  Please note the gender imbalance here: despite the number of women like me who do experience this type of cardiac event, doctors are not calling this the widowermaker, after all 
WPW – Wolff-Parkinson-White Syndrome: A condition in which an extra electrical pathway connects the atria (two upper chambers) and the ventricles (two lower chambers)  It may cause a rapid heartbeat 
NOTE FROM CAROLYN: I was very happy when we were able to include this entire glossary in my book, “A Woman’s Guide to Living with Heart Disease“ (Johns Hopkins University Press, 2017) 
Are we missing any important heart acronyms/terms from this list? Let me know!
Please can someone explain something for me  I am a 53 yr old woman and generally fit and healthy  Had 2 ECG’s due to a one off dizzy spell during a stressful time dealing with my fathers terminal diagnosis  The 2nd ECG request did give me concern as i did not know why i had to have one  On 24/01/19 at my doctors appointment she explained that on 3 the leads it showed inverted T waves  And she explained that it may suggest angina  I was so shocked  Wasn’t expecting that  She gave me a GNT (nitroglycerin) spray in case I do get pain and take 75Mg of aspirin  I’m now waiting for a Cardiology referral 
I am so stressed and consumed by what might be wrong  My maternal grandmother had angina and valve issues  Her 3 brothers all had double bypasses  Could I have inherited this? I am not overweight at 63kg and 5 ft 9  I walk 20-25 miles a week at work and general walking here and there  I started HRT (patches evorol 25 -50) in July as menopause pain was making me feel like I was 90 and was getting me down 
I am worried so much now and analysing every ache/ twinge I get  I feel like a hypochondriac at the moment  I’m worried what will happen at the cardiologist and what the test will entail and tell me  I am waiting on cholesterol test which I had on 25/01/19  Can I have inverted T waves and be fine  Please help I am so scared and crying far too much 
Hello Colleen – the first thing is: please take a big deep breath before you read another word here! I’m not a physician so of course cannot comment on your specific case, but I can tell you generally that the definition of “angina” (as this glossary lists above) is “distressing symptoms”, typically chest pain that gets worse with exertion, and goes away with rest  That’s classic stable angina… typically caused by something that’s reducing blood flow to the heart muscle (causing the chest pain of angina) 
A family history that might make a difference for you personally is only in what’s called your ‘first degree’ relatives: for example, if your mother or sister were diagnosed with heart disease before age 65, or if your Dad or brother were diagnosed before age 55, then doctors would consider that you have a family history as a risk factor for heart disease  There’s little if any scientific evidence that a grandparent or uncle’s heart disease history has any effect on your own risk 
It is a very good thing that you’re having further tests and a referral to a cardiologist, if only to ease your mind  There are many reasons for inverted T-waves, ranging from cardiac issues to completely benign conditions  One way of looking at this is choosing to believe that seeing a cardiologist will ease your mind one way or the other – so this is something to look forward to, not dread  If the cardiologist spots something suspicious, a treatment plan will be created  If not, you can wave goodbye and go back to happily living your life 
Try thinking of this cardiology appointment just as you would if your car were making some frightening noises and you were bringing it to your mechanic for a check up  You could work yourself into a complete state worrying ahead of time if the car trouble is going to be serious, or you could look at this appointment as the solution – at last! – to figuring out what’s wrong so the mechanic can recommend the next step 
Thank you for this list of so many definitions provided in plain English  what a valuable resource this is  THANK YOU, I have been looking for translations FOR PATIENTS not med school graduates– like this for three years 
My family doctor had me wear a 24 hr EKG  After reading the results, she has scheduled a scope to look inside my heart by a specialist  Completely forgoing a stress test  Said I have major changes in the EKG, what type of changes could they be looking at? Had LAD STENT INSERTED 7 YRS AGO – WHAT COULD THEY BE LOOKING FOR?
This is a great wealth of information, Carolyn! I looked and did not see my diagnosis, which is aortic stenosis  I looked under aortic as well as stenosis  Did I just miss it somehow?
I learned some new information, I am a bit familiar now, but not when I had my MI, it was like learning a new language  But, my favorite part was seeing SCAD on this list! Thank you 
Thanks and welcome! I was thinking of editing that SCAD definition actually: I suspect that that it isn’t so much that SCAD is “rare”, but it’s more that it’s “rarely correctly diagnosed” 
I totally agree that SCAD is not as rare as I believed for many years  Once awareness is spread to all medical staff, I believe many lives will be saved  Hoping for a brighter future for all SCAD patients 
I hope so too, Cathy  Perhaps when more SCAD studies (like Mayo Clinic’s) are published and read by more and more MDs, it will no longer be “rarely correctly diagnosed” 
It’s great to see IST on here  I was diagnosed with it 9 years ago and the lack of awareness is frustrating 
What a great resource for heart patients and their families!
Thanks so much, Ashley  I recently updated my original 2011 list after the world-famous Cleveland Clinic tweeted their glossary recently and I noticed that their list had a few glaring omissions (like SCAD and Brugada Syndrome) so this made me wonder what my list might be missing, too  Let me know if there’s anything else you think should be included, okay?
How is your health these days? How are you feeling?
New for me too  I have just been diagnosed with A-HCM: Apical Hypertrophic Cardiomyopathy 
I’ll add that one to my list, Kathleen – thanks!
Just saw this, Carolyn, and you’ve compiled a great resource  One note on A-HCM: Present thinking is that it’s due to a genetic modification  Runs in families though sometimes occurs spontaneously  I have not as yet done genetic testing, though it’s been offered 
Thanks Kathleen – like many cardiac diagnoses, it sounds like a moving target… Good luck to you!
This list is great  I’ve just been diagnosed and am utterly overwhelmed  Even in the WomenHeart online support community, I often have no clue most days what others are talking about with all these initials about their heart tests and specific disease  This is VERY helpful, thank you SO MUCH  Love your website which has been a godsend since my diagnosis 
Context 2: \section{Introduction}
In recent years, vehicular technology has attracted significant attention from the automotive and telecommunication industries, leading to the emergence of vehicle-to-everything (V2X) communications for improving road safety, traffic management services and driving comfort 
V2X supported by the sixth generation (6G) is envisioned to be a key enabler of future connected autonomous vehicles \cite{9779322}  Although its transformative benefits for leveraging intelligent transportation systems, V2X still face several technical issues mainly related to performance and security 

The integration of sensing and communication (ISAC) has emerged very recently as a revolutionary element of 6G that could potentially help enabling adaptive learning and intelligent decision-making in future V2X applications 
The combination of sensing and communication allows vehicles to perceive their surroundings better, predict manoeuvres from nearby users and make intelligent decisions, thus paving the way toward a safer transportation system \cite{9665433} 
Modernized vehicles are augmented with various types of sensors divided into exteroceptive to observe their surrounding environment and proprioceptive to observe their internal states 
The former like GPS, Lidar, and Cameras are conveyed to improve situational awareness, while latter sensors, such as steering, pedal, and wheel speed, convey to improve self-awareness  

While sensing the environment, vehicles can exchange messages that assist in improving situational- and self-awareness and in coordinating maneuvers with other vehicles 
Those messages like the basic safety (BSMs) and cooperative awareness messages (CAMs) are composed of transmitting vehicle's states such as position and velocity and other vehicles' states in the vicinity  Vehicles might use their sensors, such as cameras and Lidar, to detect road users (e g , pedestrians), which can be communicated with other road users via the V2X messages to improve the overall performance  However, V2X communication links carrying those messages are inherently vulnerable to malicious attacks due to the open and shared nature of the wireless spectrum among vehicles and other cellular users \cite{8336901}  For instance, a jammer in the vicinity might alter the information to be communicated to nearby vehicles/users or can intentionally disrupt communication between a platoon of vehicles making the legitimate signals unrecognizable for on-board units (OBUs) and/or road side units (RSUs) that endanger vehicular safety 
\cite{8553649} 

In addition, the integrity of GPS signals and the correct acquisition of navigation data to compute position, velocity and time information is critical in V2X applications for their safe operation  However, since civil GPS receivers rely on unencrypted satellite signals, spoofers can easily replicate them by deceiving the GPS receiver to compute falsified positions \cite{9226611} 
Also, the long distance between satellites and terrestrial GPS receivers leads to an extremely weak signal that can be easily drowned out by a spoofer  
Thus, GPS sensors' vulnerability to spoofing attacks poses a severe threat that might be causing vehicles to be out of control or even hijacked and endanger human life \cite{9881548} 
Therefore, GPS spoofing attacks and jamming interference needs to be controlled and detected in real-time to reach secured vehicular communications allowing vehicles to securely talk to each other and interact with the infrastructure (e g , roadside terminals, base stations) \cite{9860410} 

Existing methods for GPS spoofing detection include GPS signal analysis methods and GPS message encryption methods \cite{9845684}  However, the former requires the ground truth source during the detection process, which is not always possible to collect  In contrast, the latter involves support from a secured infrastructure and advanced computing resources on GPS receivers, which hinders their adoption in V2X applications  On the other hand, existing methods for jammer detection in vehicular networks are based on analysing the packet drop rate as in \cite{9484071}, making it difficult to detect an advanced jammer manipulating the legitimate signal instead of disrupting it 
In this work, we propose a method to jointly detect GPS spoofing and jamming attacks in the V2X network  A coupled generalized dynamic Bayesian network (C-GDBN) is employed to learn the interaction between RF signals received by the RSU from multiple vehicles and their corresponding trajectories  This integration of vehicles' positional information with vehicle-to-infrastructure (V2I) communications allows semantic learning while mapping RF signals with vehicles' trajectories and enables the RSU to jointly predict the RF signals it expects to receive from the vehicles from which it can anticipate the expected trajectories 

The main contributions of this paper can be summarized as follows: \textit{i)} A joint GPS spoofing and jamming detection method is proposed for the V2X scenario, which is based on learning a generative interactive model as the C-GDBN  Such a model encodes the cross-correlation between the RF signals transmitted by multiple vehicles and their trajectories, where their semantic meaning is coupled stochastically at a high abstraction level  \textit{ii)} A cognitive RSU equipped with the acquired C-GDBN can predict and estimate vehicle positions based on real-time RF signals  This allows RSU to evaluate whether both RF signals and vehicles' trajectories are evolving according to the dynamic rules encoded in the C-GDBN and, consequently, to identify the cause (i e , a jammer attacking the V2I or a spoofer attacking the satellite link) of the abnormal behaviour that occurred in the V2X environment  \textit{iii)} Extensive simulation results demonstrate that the proposed method accurately estimates the vehicles' trajectories from the predicted RF signals, effectively detect any abnormal behaviour and identify the type of abnormality occurring with high detection probabilities 
To our best knowledge, this is the first work that studies the joint detection of jamming and spoofing in V2X systems 

\section{System model and problem formulation}
The system model depicted in Fig ~\ref{fig_SystemModel}, includes a single cell vehicular network consisting of a road side unit (RSU) located at $\mathrm{p}_{R}=[{x}_{R},{y}_{R}]$, a road side jammer (RSJ) located at $\mathrm{p}_{J}=[{x}_{J},{y}_{J}]$, a road side spoofer (RSS) located at $\mathrm{p}_{s}=[{x}_{s},{y}_{s}]$ and $N$ vehicles moving along multi-lane road in an urban area  The time-varying positions of the $n$-th vehicle is given by $\mathrm{p}_{n,t}=[{x}_{n,t},{y}_{n,t}]$ where $n \in N$  Among the $K$ orthogonal subchannels available for the Vehicle-to-Infrastructure (V2I) communications, RSU assigns one V2I link to each vehicle  Each vehicle exchanges messages composed of the vehicle's state (i e , position and velocity) with RSU through the $k$-th V2I link by transmitting a signal $\textrm{x}_{t,k}$ carrying those messages at each time instant $t$ where $k \in K$  We consider a reactive RSJ that aims to attack the V2I link by injecting intentional interference to the communication link between vehicles and RSU to alter the transmitted signals by the vehicles  In contrast, the RSS purposes to mislead the vehicles by spoofing the GPS signal and so registering wrong GPS positions  RSU aims to detect both the spoofer on the satellite link and the jammer on multiple V2I links in order to take effective actions and protect the vehicular network  
The joint GPS spoofing and jamming detection problem can be formulated as the following ternary hypothesis test:
\begin{equation}
    \begin{cases}
        \mathcal{H}_{0}: \mathrm{z}_{t,k} = \mathrm{g}_{t,k}^{nR} \mathrm{x}_{t,k} + \mathrm{v}_{t,k}, \\
        \mathcal{H}_{1}: \mathrm{z}_{t,k} = \mathrm{g}_{t,k}^{nR} \mathrm{x}_{t,k} + \mathrm{g}_{t,k}^{JR} \mathrm{x}_{t,k}^{j} + \mathrm{v}_{t,k}, \\
        \mathcal{H}_{2}: \mathrm{z}_{t,k} = \mathrm{g}_{t,k}^{nR} \mathrm{x}_{t,k}^{*} + \mathrm{v}_{t,k},
    \end{cases}
\end{equation}
where $\mathcal{H}_{0}$, $\mathcal{H}_{1}$ and $\mathcal{H}_{2}$ denote three hypotheses corresponding to the absence of both jammer and spoofer, the presence of the jammer, and the presence of the spoofer, respectively  $\textrm{z}_{t,k}$ is the received signal at the RSU at $t$ over the $k$-th V2I link, $\textrm{g}_{t,k}^{nR}$ is the channel power gain from vehicle $n$ to the RSU formulated as: $\textrm{g}_{t,k}^{nR} = \alpha_{t,k}^{nR} \mathrm{h}_{t,k}^{nR}$, where $\alpha_{t,k}^{nR}$ is the large-scale fading including path-loss and shadowing modeled as \cite{8723178}: $\alpha_{t,k}^{nR}=G\beta d_{t,nR}^{-\gamma}$ 
\begin{figure}[t!]
    \centering
    \includegraphics[height=5 3cm]{Figures/SystemModel_V1 pdf}
    \caption{An illustration of the system model }
    \label{fig_SystemModel}
\end{figure}
$G$ is the pathloss constant, $\beta$ is a log normal shadow fading random variable, $d_{t,nR}=\sqrt{({x}_{n,t}-x_{R})^{2}+({y}_{n,t}-y_{R})^{2}}$ is the distance between the $n$-th vehicle and the RSU  $\gamma$ is the power decay exponent and
$\mathrm{h}_{t,k}$ is the small-scale fading component distributed according to $\mathcal{CN}(0,1)$  In addition, $\mathrm{x}_{t,k}$ is the desired signal transmitted by the $n$-th vehicle, and $\mathrm{v}_{t,k}$ is an additive white Gaussian noise with variance $\sigma_{n}^{2}$  $\mathrm{x}_{t,k}^{J}$ is the jamming signal, $\mathrm{x}_{t,k}^{*}$ is the spoofed signal (i e , the signal that carries the bits related to the wrong GPS positions), $\mathrm{g}_{t,k}^{JR} = \alpha_{t,k}^{JR} \mathrm{h}_{t,k}^{JR}$ is the channel power gain from RSJ to RSU where $\alpha_{t,k}^{JR}=G\beta d_{t,JR}^{-\gamma}$ such that $d_{t,JR}=\sqrt{({x}_{J}-x_{R})^{2}+({y}_{J}-y_{R})^{2}}$ 
We assume that the channel state information (CSI) of V2I links is known and can be estimated at the RSU as in \cite{8345717}  
The RSU is equipped with an RF antenna which can track the vehicles' trajectories after decoding the received RF signals  RSU aims to learn the interaction between the RF signals received from multiple vehicles and their corresponding trajectories 

\section{Proposed method for joint detection of GPS spoofing and jamming}

\subsection{Environment Representation}
The RSU is receiving RF signals from each vehicle and tracking its trajectory (which we refer to as GPS signal) by decoding and demodulating the received RF signals  
The Generalized state-space model describing the $i$-th signal evolvement at multiple levels embodies the following equations: 
\begin{equation} \label{eq_discreteLevel}
    \mathrm{\Tilde{S}_{t}}^{(i)} = \mathrm{f}(\mathrm{\Tilde{S}_{t-1}}^{(i)}) + \mathrm{\tilde{w}}_{t},
\end{equation}
\begin{equation} \label{eq_continuousLevel}
    \mathrm{\Tilde{X}_{t}}^{(i)} = \mathrm{A} \mathrm{\Tilde{X}_{t-1}}^{(i)} + \mathrm{B} \mathrm{U}_{\mathrm{\Tilde{S}_{t}}^{(i)}} + \mathrm{\tilde{w}}_{t},
\end{equation}
\begin{equation} \label{eq_observationLevel}
    \mathrm{\Tilde{Z}_{t}}^{(i)} = \mathrm{H} \mathrm{\Tilde{X}_{t}}^{(i)} + \mathrm{\tilde{v}}_{t},
\end{equation}
where $i \in \{$RF, GPS$\}$ indicates the type of signal received by the RSU  The transition system model defined in \eqref{eq_discreteLevel} explains the evolution of the discrete random variables $\mathrm{\Tilde{S}_{t}}^{(i)}$ representing the clusters of the RF (or GPS) signal dynamics, $\mathrm{f}( )$ is a non linear function of its argument and the additive term $\mathrm{\tilde{w}}_{t}$ denotes the process noise  The dynamic model defined in \eqref{eq_continuousLevel} explains the RF signal dynamics evolution or the motion dynamics evolution of the $n$-th vehicle, where $\mathrm{\Tilde{X}_{t}}^{(i)}$ are hidden continuous variables generating sensory signals, $\mathrm{A} \in \mathbb{R}^{2d}$ and $\mathrm{B} \in \mathbb{R}^{2d}$ are the dynamic and control matrices, respectively, and $\mathrm{U}_{\mathrm{\Tilde{S}_{t}}^{(i)}}$ is the control vector representing the dynamic rules of how the signals evolve with time  The measurement model defined in \eqref{eq_observationLevel} describes dependence of the sensory signals $\mathrm{\Tilde{Z}_{t}}^{(i)}$ on the hidden states $\mathrm{\Tilde{X}_{t}}^{(i)}$ that is parametrized by the measurement matrix $\mathrm{B} \in \mathbb{R}^{2d}$ where $d$ stands for the data dimensionality and $\mathrm{\tilde{v}}_{t}$ is a random noise  

\subsection{Learning GDBN}
The hierarchical dynamic models defined in \eqref{eq_discreteLevel}, \eqref{eq_continuousLevel} and \eqref{eq_observationLevel} are structured in a Generalized Dynamic Bayesian Network (GDBN) \cite{9858012} as shown in Fig ~\ref{fig_GDBN_CGDBN}-(a) that provides a probabilistic graphical model expressing the conditional dependencies among random hidden variables and observable states  The generative process explaining how sensory signals have been generated can be factorized as:
\begin{equation} \label{eq_generative_process}
\begin{split}
    \mathrm{P}(\mathrm{\tilde{Z}}_{t}^{(i)}, \mathrm{\tilde{X}}_{t}^{(i)}, \mathrm{\tilde{S}}_{t}^{(i)}) = \mathrm{P}(\mathrm{\tilde{S}}_{0}^{(i)}) \mathrm{P}(\mathrm{\tilde{X}}_{0}^{(i)}) \\ \bigg[ \prod_{t=1}^{\mathrm{T}} \mathrm{P}(\mathrm{\tilde{Z}}_{t}^{(i)}|\mathrm{\tilde{X}}_{t}^{(i)}) \mathrm{P}(\mathrm{\tilde{X}}_{t}^{(i)}|\mathrm{\tilde{X}}_{t-1}^{(i)}, \mathrm{\tilde{S}}_{t}^{(i)}) \mathrm{P}(\mathrm{\tilde{S}}_{t}^{(i)}|\mathrm{\tilde{S}}_{t-1}^{(i)}) \bigg],
\end{split}
\end{equation}
where $\mathrm{P}(\mathrm{\tilde{S}}_{0}^{(i)})$ and $\mathrm{P}(\mathrm{\tilde{X}}_{0}^{(i)})$ are initial prior distributions, $\mathrm{P}(\mathrm{\tilde{Z}}_{t}^{(i)}|\mathrm{\tilde{X}}_{t}^{(i)})$ is the likelihood, $\mathrm{P}(\mathrm{\tilde{X}}_{t}^{(i)}|\mathrm{\tilde{X}}_{t-1}^{(i)}, \mathrm{\tilde{S}}_{t}^{(i)})$ and $\mathrm{P}(\mathrm{\tilde{S}}_{t}^{(i)}|\mathrm{\tilde{S}}_{t-1}^{(i)})$ are the transition densities describing the temporal and hierarchical dynamics of the generalized state-space model 
The generative process defined in \eqref{eq_generative_process} indicates the cause-effect relationships the model impose on the random variables $\mathrm{\tilde{S}}_{t}^{(i)}$, $\mathrm{\tilde{X}}_{t}^{(i)}$ and $\mathrm{\tilde{Z}}_{t}^{(i)}$ forming a chain of causality describing how one state contributes to the production of another state which is represented by the link $\mathrm{\tilde{S}}_{t}^{(i)} \rightarrow \mathrm{\tilde{X}}_{t}^{(i)} \rightarrow \mathrm{\tilde{Z}}_{t}^{(i)}$ 

The RSU starts perceiving the environment using a static assumption about the environmental states evolution by assuming that sensory signals are only subject to random noise  Hence, RSU predicts the RF signal (or vehciles trajectory) using the following simplified model:
$\mathrm{\tilde{X}}_{t}^{(i)} = \mathrm{A} \mathrm{\tilde{X}}_{t-1}^{(i)} + \mathrm{\tilde{w}}_{t}$, 
that differs from \eqref{eq_continuousLevel} in the control vector $\mathrm{U}_{\mathrm{\Tilde{S}_{t}}^{(i)}}$ which is supposed to be null, i e , $\mathrm{U}_{\mathrm{\Tilde{S}_{t}}^{(i)}} = 0$ as the dynamic rules explaining how the environmental states evolve with time are not discovered yet 
Those rules can be discovered by exploiting the generalized errors (GEs), i e , the difference between predictions and observations  The GEs projected into the measurement space are calculated as:
$\tilde{\varepsilon}_{\mathrm{\tilde{Z}}_{t}^{(i)}}^{} = \mathrm{\tilde{Z}}_{t}^{(i)} - \mathrm{H} \mathrm{\tilde{X}}_{t}^{(i)}$ 
Projecting $\tilde{\varepsilon}_{\mathrm{\tilde{Z}}_t}^{}$ back into the generalized state space can be done as follows:
\begin{equation}\label{GE_continuousLevel_initialModel}
    \tilde{\varepsilon}_{\mathrm{\tilde{X}}_t}^{(i)} = \mathrm{H}^{-1}\tilde{\varepsilon}_{\mathrm{\tilde{Z}}_{t}^{(i)}}^{}=\mathrm{H}^{-1}(\mathrm{\tilde{Z}}_{t}^{(i)}-\mathrm{H}\mathrm{\tilde{X}}_{t}^{(i)}) = \mathrm{H}^{-1}\mathrm{\tilde{Z}}_{t}^{(i)} - \mathrm{\tilde{X}}_{t}^{(i)} 
\end{equation}
The GEs defined in \eqref{GE_continuousLevel_initialModel} can be grouped into discrete clusters in an unsupervised manner by employing the Growing Neural Gas (GNG)  The latter produces a set of discrete variables (clusters) denoted by:
$\mathbf{\tilde{S}^{(i)}}=\{\mathrm{\tilde{S}}_{1}^{(i)},\mathrm{\tilde{S}}_{2}^{(i)},\dots,\mathrm{\tilde{S}}_{M_{i}}^{(i)}\}$,
where $M_{i}$ is the total number of clusters and each cluster $\mathrm{\tilde{S}}_{m}^{(i)} \in \mathbf{\tilde{S}^{(i)}}$ follows a Gaussian distribution composed of GEs with homogeneous properties, such that $\mathrm{\tilde{S}}_{m}^{(i)} \sim \mathcal{N}(\tilde{\mu}_{\mathrm{\tilde{S}}_{m}^{(i)}}=[\mu_{\tilde{S}_{m}^{(i)}}, \Dot{\mu}_{\tilde{S}_{m}^{(i)}}], \Sigma_{\mathrm{\tilde{S}}_{m}^{(i)}})$ 
\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 40\linewidth}
        \centering
           \includegraphics[width=2 5cm]{Figures/GDBN pdf}
        \\[-1 0mm]
        {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{ 50\linewidth}
            \centering
            \includegraphics[width=5 0cm]{Figures/C_GDBN pdf}
           
            {\scriptsize (b)}
        \end{minipage}
        \caption{(a) The GDBN  (b) The coupled GDBN (C-GDBN) composed of two GDBNs representing the two signals received at the RSU where their discrete hidden variables are stochastically coupled }
        \label{fig_GDBN_CGDBN}
    \end{center}
\end{figure}
The dynamic transitions of the sensory signals among the available clusters can be captured in a time-varying transition matrix ($\Pi_{\tau}$) by estimating the time-varying transition probabilities $\pi_{ij}=\mathrm{P}(\mathrm{\tilde{S}}_{t}^{(i)}=i|\mathrm{\tilde{S}}_{t-1}^{(i)}=j, \tau)$ where $\tau$ is the time spent in $\mathrm{\tilde{S}}_{t-1}^{(i)}=j$ before transition to $\mathrm{\tilde{S}}_{t}^{(i)}=i$ 

\subsection{Learning Coupled GDBN (C-GDBN)}
The learning procedure described in the previous section can be executed for each signal type, i e , RF and GPS  After learning a separated GDBN model for each signal type, we analyse the interaction behaviour between RF signal and GPS signal received at the RSU by tracking the cluster firing among $\mathbf{\tilde{S}^{(1)}}$ and $\mathbf{\tilde{S}^{(2)}}$ during a certain experience  Such an interaction can be encoded in a Coupled GDBN (C-GDBN) as shown in Fig \ref{fig_GDBN_CGDBN}-(b) composed of the two GDBNs representing the two signals where their hidden variables at the discrete level are stochastically coupled (in $\mathrm{\tilde{C}}_{t}{=}[\mathrm{\tilde{S}}_{t}^{(1)},\mathrm{\tilde{S}}_{t}^{(2)}]$) as those variables are uncorrelated but have coupled means 
The interactive matrix $\Phi \in \mathbb{R}^{M_{1},M_{2}}$ encodes the firing cluster pattern allowing to predict the GPS signal from RF signal is defined as follows:
\begin{equation} \label{interactiveTM_fromRFtoGPS}
\Phi = 
        \begin{bmatrix} 
            \mathrm{P}(\mathrm{\Tilde{S}_{1}}^{(2)}|\mathrm{\Tilde{S}_{1}}^{(1)}) & \mathrm{P}(\mathrm{\Tilde{S}_{2}}^{(2)}|\mathrm{\Tilde{S}_{1}}^{(1)}) & \dots & \mathrm{P}(\mathrm{\Tilde{S}_{M_{2}}}^{(2)}|\mathrm{\Tilde{S}_{1}}^{(1)}) \\
            \mathrm{P}(\mathrm{\Tilde{S}_{1}}^{(2)}|\mathrm{\Tilde{S}_{2}}^{(1)}) & \mathrm{P}(\mathrm{\Tilde{S}_{2}}^{(2)}|\mathrm{\Tilde{S}_{2}}^{(1)}) & \dots & \mathrm{P}(\mathrm{\Tilde{S}_{M_{2}}}^{(2)}|\mathrm{\Tilde{S}_{2}}^{(1)}) \\
            \vdots & \vdots & \ddots & \vdots \\
            \mathrm{P}(\mathrm{\Tilde{S}_{1}}^{(2)}|\mathrm{\Tilde{S}_{M_{1}}}^{(1)}) & \mathrm{P}(\mathrm{\Tilde{S}_{2}}^{(2)}|\mathrm{\Tilde{S}_{M_{1}}}^{(1)}) & \dots & \mathrm{P}(\mathrm{\Tilde{S}_{M_{2}}}^{(2)}|\mathrm{\Tilde{S}_{M_{1}}}^{(1)}) 
        \end{bmatrix} 
\end{equation}

\subsection{Joint Prediction and Perception}
RSU starts predicting the RF signals it expects to receive from each vehicle based on a Modified Markov Jump Particle Filter (M-MJPF) \cite{9858012} that combines Particle filter (PF) and Kalman filter (KF) to perform temporal and hierarchical predictions  Since the acquired C-GDBN allows predicting a certain signal's dynamic evolution based on another's evolution, it requires an interactive Bayesian filter capable of dealing with more complicated predictions  To this purpose, we propose to employ an Interactive M-MJPF (IM-MJPF) on the C-GDBN  The IM-MJPF consists of a PF that propagates a set of $L$ particles equally weighted, such that $\{\mathrm{\tilde{S}}_{t,l}^{(1)}, \mathrm{W}_{t,l}^{(1)}\}{\sim}\{\pi(\mathrm{\tilde{S}}_{t}^{(1)}), \frac{1}{L}\}$, where $\mathrm{\tilde{S}}_{t,l}^{(1)}$, $l \in L$ and $( ^{(1)})$ is the RF signal type  In addition, RSU relies on $\Phi$ defined in \eqref{interactiveTM_fromRFtoGPS} to predict $\mathrm{\tilde{S}}_{t}^{(2)}$ realizing the discrete cluster of vehicle's trajectory starting from the predicted RF signal according to: $\{\mathrm{\tilde{S}}_{t}^{(2)},\mathrm{W}_{t,l}^{(2)}\}{\sim} \{\Phi(\mathrm{\tilde{S}}_{t,l}^{(1)}){=}\mathrm{P}( |\mathrm{\tilde{S}}_{t,l}^{(1)}), \mathrm{W}_{t,l}^{(2)}\}$  For each predicted discrete variable $\mathrm{\tilde{S}}_{t,l}^{(i)}$, a multiple KF is employed to predict multiple continuous variables which guided by the predictions at the higher level as declared in \eqref{eq_continuousLevel} that can be represented probabilistically as $\mathrm{P}(\mathrm{\tilde{X}}_{t}^{(i)}|\mathrm{\tilde{X}}_{t-1}^{(i)}, \mathrm{\tilde{S}}_{t}^{(i)})$  The posterior probability that is used to evaluate expectations is given by:
\begin{multline} \label{piX}
    \pi(\mathrm{\tilde{X}}_{t}^{(i)})=\mathrm{P}(\mathrm{\tilde{X}}_{t}^{(i)},\mathrm{\tilde{S}}_{t}^{(i)}|\mathrm{\tilde{Z}}_{t-1}^{(i)})= \\ \int \mathrm{P}(\mathrm{\tilde{X}}_{t}^{(i)}|\mathrm{\tilde{X}}_{t-1}^{(i)}, \mathrm{\tilde{S}}_{t}^{(i)}) \lambda(\mathrm{\tilde{X}}_{t-1}^{(i)})d\mathrm{\tilde{X}}_{t-1}^{(i)},
\end{multline}
where $\lambda(\mathrm{\tilde{X}}_{t-1}^{(i)}){=}\mathrm{P}(\mathrm{\tilde{Z}}_{t-1}^{(i)}|\mathrm{\tilde{X}}_{t-1}^{(i)})$  
The posterior distribution can be updated (and so representing the updated belief) after having seen the new evidence $\mathrm{\tilde{Z}}_{t}^{(i)}$ by exploiting the diagnostic message $\lambda(\mathrm{\tilde{X}}_{t}^{(i)})$ in the following form: $\mathrm{P}(\mathrm{\tilde{X}}_{t}^{(i)}, \mathrm{\tilde{S}}_{t}^{(i)}|\mathrm{\tilde{Z}}_{t}^{(i)}) {=} \pi(\mathrm{\tilde{X}}_{t}^{(i)})\lambda(\mathrm{\tilde{X}}_{t}^{(i)})$  Likewise, belief in discrete hidden variables can be updated according to: $\mathrm{W}_{t,l}^{(i)}{=}\mathrm{W}_{t,l}^{(i)}\lambda (\mathrm{\tilde{S}}_{t}^{(i)})$ where:
$\lambda (\mathrm{\tilde{S}}_{t}^{(i)}) {=} \lambda (\mathrm{\Tilde{X}}_{t}^{(i)})\mathrm{P}(\mathrm{\Tilde{X}}_{t}^{(i)}|\mathrm{\tilde{S}}_{t}^{(i)}) {=} \mathrm{P}(\mathrm{\tilde{Z}}_{t}^{(i)}|\mathrm{\Tilde{X}}_{t}^{(i)})\mathrm{P}(\mathrm{\Tilde{X}}_{t}^{(i)}|\mathrm{\tilde{S}}_{t}^{(i)})$ 

\subsection{Joint GPS spoofing and jamming detection}
RSU can evaluate the current situation and identify if V2I is under attack, or the satellite link is under spoofing based on a multiple abnormality indicator produced by the IM-MJPF  The first indicator calculates the similarity between the predicted RF signal and the observed one, which is defined as:
\begin{equation}\label{eq_CLA1}
    \Upsilon_{\mathrm{\tilde{X}}_{t}^{(1)}} = -ln \bigg( \mathcal{BC} \big(\pi(\mathrm{\tilde{X}}_{t}^{(1)}),\lambda(\mathrm{\tilde{X}}_{t}^{(1)}) \big) \bigg),
\end{equation}
where $\mathcal{BC}( ){=}\int \sqrt{\pi(\mathrm{\tilde{X}}_{t}^{(1)}),\lambda(\mathrm{\tilde{X}}_{t}^{(1)}})d\mathrm{\tilde{X}}_{t}^{(1)}$ is the Bhattacharyya coefficient 
The second indicator calculates the similarity between the predicted GPS signal (from the RF signal) and the observed one after decoding the RF signal which is defined as:
\begin{equation}\label{eq_CLA2}
    \Upsilon_{\mathrm{\tilde{X}}_{t}^{(2)}} = -ln \bigg( \mathcal{BC} \big(\pi(\mathrm{\tilde{X}}_{t}^{(2)}),\lambda(\mathrm{\tilde{X}}_{t}^{(2)}) \big) \bigg),
\end{equation}
where $\mathcal{BC}( ){=}\int \sqrt{\pi(\mathrm{\tilde{X}}_{t}^{(2)}),\lambda(\mathrm{\tilde{X}}_{t}^{(2)}})d\mathrm{\tilde{X}}_{t}^{(2)}$ 
Different hypotheses can be identified by the RSU to understand the current situation whether there is: a jammer attacking the V2I link, or a spoofer attacking the link between the satellite and the vehicle or both jammer and spoofer are absent according to:
\begin{equation}
    \begin{cases}
        \mathcal{H}_{0}: \text{if} \ \ \Upsilon_{\mathrm{\tilde{X}}_{t}^{(1)}} < \xi_{1} \ \text{and} \ \Upsilon_{\mathrm{\tilde{X}}_{t}^{(2)}} < \xi_{2}, \\
        \mathcal{H}_{1}: \text{if} \ \ \Upsilon_{\mathrm{\tilde{X}}_{t}^{(1)}} \geq \xi_{1} \ \text{and} \ \Upsilon_{\mathrm{\tilde{X}}_{t}^{(2)}} \geq \xi_{2}, \\
        \mathcal{H}_{2}: \text{if} \ \ \Upsilon_{\mathrm{\tilde{X}}_{t}^{(1)}} < \xi_{1} \ \text{and} \ \Upsilon_{\mathrm{\tilde{X}}_{t}^{(2)}} \geq \xi_{2},
    \end{cases}
\end{equation}
where $\xi_{1} = \mathbb{E}[\Bar{\Upsilon}_{\mathrm{\tilde{X}}_{t}^{(1)}}] + 3\sqrt{\mathbb{V}[\Bar{\Upsilon}_{\mathrm{\tilde{X}}_{t}^{(1)}}]}$, and $\xi_{2} = \mathbb{E}[\Bar{\Upsilon}_{\mathrm{\tilde{X}}_{t}^{(2)}}] + 3\sqrt{\mathbb{V}[\Bar{\Upsilon}_{\mathrm{\tilde{X}}_{t}^{(2)}}]}$  In $\xi_{1}$ and $\xi_{2}$, $\Bar{\Upsilon}_{\mathrm{\tilde{X}}_{t}^{(1)}}$ and $\Bar{\Upsilon}_{\mathrm{\tilde{X}}_{t}^{(2)}}$ stand for the abnormality signals during training (i e , normal situation when jammer and spoofer are absent) 

\subsection{Evaluation metrics}
In order to evaluate the performance of the proposed method to jointly detect jammer and GPS spoofer, we adopt the jammer detection probability ($\mathrm{P}_{d}^{j}$) and the spoofer detection probability ($\mathrm{P}_{d}^{s}$), respectively, which are defined as:
\begin{equation}
    \mathrm{P}_{d}^{j} = \mathrm{Pr}(\Upsilon_{\mathrm{\tilde{X}}_{t}^{(1)}}\geq \xi_{1}, \Upsilon_{\mathrm{\tilde{X}}_{t}^{(2)}} \geq \xi_{2}|\mathcal{H}_{1}),
\end{equation}
\begin{equation}
    \mathrm{P}_{d}^{s} = \mathrm{Pr}(\Upsilon_{\mathrm{\tilde{X}}_{t}^{(1)}}< \xi_{1}, \Upsilon_{\mathrm{\tilde{X}}_{t}^{(2)}} \geq \xi_{2}|\mathcal{H}_{2}) 
\end{equation}
Also, we evaluate the accuracy of the proposed method in predicting and estimating the vehicles' trajectories and the expected RF signals by adopting the root mean square error (RMSE) defined as:
\begin{equation}
    RMSE = \sqrt{ \frac{1}{T} \sum_{t=1}^{T}\bigg( \mathrm{\tilde{Z}}_{t}^{(i)}-\mathrm{\tilde{X}}_{t}^{(i)} \bigg)^{2} },
\end{equation}
where $T$ is the total number of predictions 

\section{Simulation Results}
In this section, we evaluate the performance of the proposed method to jointly detect the jammer and the spoofer using extensive simulations  We consider $\mathrm{N}=2$ vehicles interacting inside the environment and exchanging their states (i e , position and velocity) with the RSU  The vehicles move along predefined trajectories performing various maneuvers which are picked from the \textit{Lankershim} dataset proposed by \cite{5206559}  The dataset depicts a four way intersection and includes about $19$ intersection maneuvers  RSU assigns one subchannel realizing the V2I link for each vehicle over which the vehicles' states are transmitted  The transmitted signal carrying the vehicle's state and the jamming signal are both QPSK modulated  
The simulation settings are: carrier frequency of $2$GHz, BW${=}1 4$MHz, cell radius of $500$m, RSU antenna height and gain is $25$m and $8$ dBi, receiver noise figure of $5$dB, vehicle antenna height and gain is $1 5$m and $3$dBi, vehicle speed is $40$Km/h, V2I transmit power is $23$dBm, jammer transmit power ranging from $20$dBm to $40$dBm, SNR of $20$dB, path loss model ($128 1{+}37 6log d$), Log-normal shadowing with $8$dB standard deviation and a fast fading channel following the Rayleigh distribution 
\begin{figure}[ht!]
    \begin{center}
        \begin{minipage}[b]{ 55\linewidth}
        \centering
            \includegraphics[width=5 0cm]{Results/ObservedTrajectories_reference}
        \\[-1 5mm]
        {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
            \includegraphics[width=4 9cm]{Results/ObservedRFsignal_Veh1_reference}
            \\[-1 5mm]
            {\scriptsize (b)}
        \end{minipage}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
            \includegraphics[width=4 9cm]{Results/ObservedRFsignal_Veh2_reference}
            \\[-1 5mm]
            {\scriptsize (c)}
        \end{minipage}
        \caption{An example visualizing the received RF signals from the two vehicles and the corresponding trajectories: (a) Vehicles' trajectories, (b) received RF signal from vehicle 1, (c) received RF signal from vehicle 2 }
        \label{fig_receivedRFsignalandTrajectory}
    \end{center}
\end{figure}
\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
                \includegraphics[width=4 5cm]{Results/clusters_trajectory_veh1}
            \\[-1 5mm]
            {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
                \includegraphics[width=4 5cm]{Results/clusters_trajectory_veh2}
            \\[-1 5mm]
            {\scriptsize (b)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 5cm]{Results/clusters_RFsignal_veh1}
            \\[-1 5mm]
            {\scriptsize (c)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 5cm]{Results/clusters_RFsignal_veh2}
            \\[-1 5mm]
            {\scriptsize (d)}
        \end{minipage}
       
        \caption{GNG output after clustering the generalized errors obtained from different experiences: (a) clustered trajectory of vehicle 1, (b) clustered trajectory of vehicle 2, (c) clustered RF signal received from vehicle 1, (d) clustered RF signal received from vehicle 2 }
        \label{fig_GNG_of_receivedRFsignalandTrajectory}
    \end{center}
\end{figure}

The RSU aims to learn multiple interactive models (i e , C-GDBN models) encoding the cross relationship between the received RF signal from each vehicle and its corresponding trajectory  These models allow the RSU to predict the trajectory the vehicle will follow based on the received RF signal and evaluate whether the V2I is under jamming attacks or the satellite link is under spoofing  It is to note that the RSU is receiving only the RF signals from the two vehicles and obtaining their positions after decoding the RF signals  Thus, the RSU should be able to evaluate if the received RF signals are evolving according to the dynamic rules learned so far and if the vehicles are following the expected (right) trajectories to decide whether the V2I links are really under attack or whether the satellite link is under spoofing 

Fig ~\ref{fig_receivedRFsignalandTrajectory}-(a) illustrates an example of the interaction between the two vehicles performing a particular manoeuvre, and Fig ~\ref{fig_receivedRFsignalandTrajectory}-(b) shows the received RF signals by the RSU from the two vehicles  At the beginning of the learning process, RSU performs predictions according to the simplified model defined in \eqref{eq_continuousLevel} where $\mathrm{U}_{\mathrm{\Tilde{S}_{t}}^{(i)}} {=} 0$ 
After obtaining the generalized errors as pointed out in \eqref{GE_continuousLevel_initialModel}, RUS clusters those errors using GNG to learn two GDBN models encoding the dynamic rules of how the RF signal and the GPS signal evolve with time, respectively, as showed in Fig ~\ref{fig_GNG_of_receivedRFsignalandTrajectory} and Fig ~\ref{fig_graphicalRep_transitionMatrices}  RSU can couple the two GDBNs by learning the interactive transition matrix that is encoded in a C-GDBN as shown in Fig ~\ref{fig_interactiveMatrices} 
\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
                \includegraphics[width=4 5cm]{Results/graphTransition_Trajectory_veh1}
            \\[-1 5mm]
            {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
                \includegraphics[width=4 5cm]{Results/graphTransition_Trajectory_veh2}
            \\[-1 5mm]
            {\scriptsize (b)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 5cm]{Results/graphTransition_RFsignal_veh1}
            \\[-1 5mm]
            {\scriptsize (c)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 5cm]{Results/graphTransition_RFsignal_veh2}
            \\[-1 5mm]
            {\scriptsize (d)}
        \end{minipage}
        \caption{Graphical representation of the transition matrices (TM): (a) TM related to the trajectory of vehicle 1, (b) TM related to the trajectory of vehicle 2, (c) TM related to the RF signal received from vehicle 1, (d) TM related to the RF signal received from vehicle 2 }
        \label{fig_graphicalRep_transitionMatrices}
    \end{center}
\end{figure}
\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
                \includegraphics[width=3 8cm]{Results/interactiveMatrix_RFtoGPS_Neu5_veh1}
            \\[-1 0mm]
            {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=3 8cm]{Results/interactiveMatrix_RFtoGPS_Neu25_veh1}
            \\[-1 0mm]
            {\scriptsize (d)}
        \end{minipage}
       
        \caption{Interactive transition matrix defined in \eqref{interactiveTM_fromRFtoGPS} using different configurations: (a) $\mathrm{M_{1}}=5$, $\mathrm{M_{2}}=5$, (b) $\mathrm{M_{1}}=25$, $\mathrm{M_{2}}=25$ }
        \label{fig_interactiveMatrices}
    \end{center}
\end{figure}
\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 49\linewidth}
        \centering
            \includegraphics[width=4 9cm]{Results/RF_situation1_best_veh1}
        \\[-1 5mm]
        {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 9cm]{Results/RF_situation1_worst_veh1}
            \\[-1 5mm]
            {\scriptsize (b)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 9cm]{Results/RF_situation1_best_veh2}
            \\[-1 5mm]
            {\scriptsize (c)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 9cm]{Results/RF_situation1_worst_veh2}
            \\[-1 5mm]
            {\scriptsize (d)}
        \end{minipage}
        \caption{An example visualizing the predicted and observed RF signals transmitted by the 2 vehicles using different configurations  Predicted RF signal from: (a) vehicle 1 using $\mathrm{M_{1}}{=}5$, $\mathrm{M_{2}}{=}5$, (b) vehicle 1 using $\mathrm{M_{1}}{=}25$, $\mathrm{M_{2}}{=}25$, (c) vehicle 2 using $\mathrm{M_{1}}{=}5$, $\mathrm{M_{2}}{=}5$, (d) vehicle 2 using $\mathrm{M_{1}}{=}25$, $\mathrm{M_{2}}{=}25$ }
            \label{fig_situation1_PredictedRF}
    \end{center}
\end{figure}

\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 49\linewidth}
        \centering
            \includegraphics[width=4 8cm]{Results/GPSfromRF_situation1_best}
        \\[-1 0mm]
        {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 8cm]{Results/GPSfromRF_situation1_worst}
            \\[-1 0mm]
            {\scriptsize (b)}
        \end{minipage}
        %
        \caption{An example visualizing the predicted and observed trajectories of two vehicles interacting in the environment  (a) $\mathrm{M_{1}}{=}5$, $\mathrm{M_{2}}{=}5$, (b) $\mathrm{M_{1}}{=}25$, $\mathrm{M_{2}}{=}25$ }
            \label{fig_situation1_VehiclesTrajectories}
    \end{center}
\end{figure}

\begin{figure}[ht!]
    \begin{center}
        \begin{minipage}[b]{ 49\linewidth}
        \centering
            \includegraphics[width=4 8cm]{Results/rmse_on_trajectory}
        \\[-1 0mm]
        {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 8cm]{Results/rmse_on_RFSignal}
            \\[-1 0mm]
            {\scriptsize (b)}
        \end{minipage}
        \caption{The average RMSE after testing different experiences and examples of: (a) trajectories and (b) RF signals }
            \label{fig_rmse_onTraj_onSig}
    \end{center}
\end{figure}

Fig ~\ref{fig_situation1_PredictedRF} illustrates an example comparing between predicted RF signals and observed ones based on two different configurations in learning the interactive matrix (as shown in Fig ~\ref{fig_interactiveMatrices})  Also, Fig ~\ref{fig_situation1_VehiclesTrajectories} illustrates an example comparing between the predicted and observed trajectories of the two vehicles using the two interactive matrices depicted in Fig ~\ref{fig_interactiveMatrices}  From Fig ~\ref{fig_situation1_PredictedRF} and Fig ~\ref{fig_situation1_VehiclesTrajectories} we can see that using an interactive matrix with less clusters allows to perform better predictions compared to that with more clusters  This can be validated by observing Fig ~\ref{fig_rmse_onTraj_onSig} that illustrates the RMSE values versus different number of clusters related to the two models representing the dynamics of the received RF signals and the vehicles' trajectories  It can be seen that as the number of clusters increases the RMSE error increases, since adding more clusters decreases the firing probability that explains the possibility to be in one of the $M_{2}$ clusters of the second model conditioned in being in a certain cluster of the first model 

Fig ~\ref{fig_exNormal_Spoofed_JammedTrajectories} illustrates an example of vehicle's trajectory under normal situation (i e , jammer and spoofer are absent), under jamming attacks and under spoofing attacks  Also the figure shows the predicted trajectory which should follow the same dynamic rules learned during a normal situation  After that, we implemented the IM-MJPF on the learned C-GDBN to perform multiple predictions, i e , to predict the RF signal that the RSU is expecting to receive from a certain vehicle and the corresponding trajectory that the vehicle is supposed to follow  IM-MJPF through the comparison between multiple predictions and observations, produces multiple abnormality signals as defined in \eqref{eq_CLA1} and \eqref{eq_CLA2} which are used to detect the jammer and the spoofer 

Fig ~\ref{fig_abnormalitySignals_JammerSpoofer} illustrates the multiple abnormality signals related to the example shown in Fig ~\ref{fig_exNormal_Spoofed_JammedTrajectories}  We can observe that the abnormal signals related to both RF signal (Fig ~\ref{fig_abnormalitySignals_JammerSpoofer}-(a)) and trajectory (Fig ~\ref{fig_abnormalitySignals_JammerSpoofer}-(b)) are below the threshold under normal situations  This proves that RSU learned the correct dynamic rules of how RF signals and trajectories evolve when the jammer and spoofer are absent (i e , under normal situations)  Also, we can see that the RSU can notice a high deviation on both the RF signal and the corresponding trajectory due to a jamming interference from what it has learned so far by relying on the abnormality signals  In contrast, we can see that under spoofing attacks, RSU notice a deviation only on the trajectory and not on the RF signal since the spoofer has affected only the positions without manipulating the RF signal  In addition, it is obvious how the proposed method allows the RSU to identify the type of abnormality occurring and to explain the cause of the detected abnormality (i e , understanding if it was because of a jammer attacking the V2I link or a spoofer attacking the satellite link) 
\begin{figure}[t!]
    \centering
    \includegraphics[width=6 5cm]{Results/trajectories_underJamming_andSpoofing}
   
    \caption{Vehicle's trajectory under: normal situation, jamming and spoofing }
    \label{fig_exNormal_Spoofed_JammedTrajectories}
\end{figure}
\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 92\linewidth}
        \centering
            \includegraphics[height=2 6cm]{Results/abnSignal_onRF}
        \\[-1 5mm]
        {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{ 92\linewidth}
            \centering
            \includegraphics[height=2 6cm]{Results/abnSignal_onGPS}
            \\[-1 5mm]
            {\scriptsize (b)}
        \end{minipage}
        %
        \caption{Abnormality Signals related to the example shown in Fig \ref{fig_exNormal_Spoofed_JammedTrajectories}: (a) abnormality indicators related to the RF signal, (b) abnormality indicators related to the trajectory }
            \label{fig_abnormalitySignals_JammerSpoofer}
    \end{center}
\end{figure}
\begin{figure}[t!]
    \centering
    \includegraphics[height=3 2cm]{Results/Detection_Probability_RFfromGPS_versusPj}
    \caption{Detection probability ($\mathrm{P_{d}}$) versus jammer's power ($\mathrm{P_{J}}$) using different number of clusters $\mathrm{M}_{2}$ }
    \label{fig_jammerDetectionProb}
\end{figure}
\begin{figure}[t!]
    \centering
    \includegraphics[height=3 2cm]{Results/spoofingDetectionProbability_falseAlarm_versusM2}
    \caption{Spoofing detection probability ($\mathrm{P}_{d}^{s}$) and spoofing false alarm ($\mathrm{P}_{f}^{s}$) versus the number of clusters $\mathrm{M}_{2}$ }
    \label{fig_spooferDetectionProb}
\end{figure}

Fig ~\ref{fig_jammerDetectionProb} shows the overall performance of the proposed method in detecting the jammer by testing many situations and examples and by considering different jamming powers which ranges from $20$dBm to $40$dBm  It can be seen that the proposed method is able to detect the jammer with high probabilities (near $1$) and by considering low and high jamming powers  Also, the figure compares the performance in detecting the jammer by varying the number of clusters ($M_{2}$) 
Fig ~\ref{fig_spooferDetectionProb} shows the overall performance of the proposed method in detecting the spoofer by testing different different examples of driving maneuvers  It can be seen that the RSU is able to detect the spoofer with high detection probability and null false alarm versus different number of clusters 

\section{Conclusion}
A joint detection method of GPS spoofing and jamming attacks is proposed  The method is based on learning a dynamic interactive model encoding the cross-correlation between the received RF signals from multiple vehicles and their corresponding trajectories  Simulation results show the high effectiveness of the proposed approach in jointly detecting the GPS spoofer and jammer attacks  
Subsequent work will extend the system model to consider more than two vehicles with different channel conditions and various modulation schemes to evaluate the effectiveness of the proposed method 

\bibliographystyle{IEEEtran}




ground_truth: Implantable Cardioverter Defibrillator (ICD) is a surgically implanted electronic device to treat life-threatening heartbeat irregularities.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the name of the generative interactive model used in the method?

Read the following text and answer briefly.

Context 3: \section*{Dynamical Behaviour of $O$ in Lattice Gases}

The dynamical behaviour of the anisotropic order parameter  $m$ [see Eq ~\eqref{eq:def-m} in the Letter] following a quench to the critical point is well described by
the Gaussian theory for all the three lattice gas models studied, $i e ,$ driven lattice gas with either constant (IDLG) or random (RDLG) infinite drive and equilibrium lattice gas (LG)  In other words, in the short-time regime, $m \sim t^{1/2}$ [see Eq  \eqref{eq:mt}] and the Binder cumulant $g$ of the lowest transverse mode [defined in Eq  \eqref{eq:binder}] is zero in this regime  The alternative order parameter $O,$ however, distinguishes between the driven (IDLG, RDLG) and the equilibrium (LG) lattice gases  

In order to understand  this, we first write the phenomenological scaling form for $O$,  analogous to Eq  \eqref{eq:scalingass} in  the Letter,
\begin{eqnarray}
O (t, L_{\parallel} ; S_\Delta) = L_{\parallel}^{-\beta/[\nu(1+\Delta)]} \tilde f_O (t/L_{\parallel}^{z/(1+\Delta)} ; S_\Delta) \quad
\label{eq:Oscalingass}
\end{eqnarray}
We already remarked that, in the LG, this scaling form is not compatible with the prediction $O \sim t^{1/8}  L_{\parallel}^{-1/2}$ of the Gaussian theory   However, following Ref  \cite{AS2002}, it can be argued that, at short times, the only dependence of $O$ on the system size $L_{\parallel}$ is of the form $O \sim L_\parallel^{-1/2}$ which is very well confirmed by numerical simulations  Accordingly,  the generic behaviour of $O$ can be assumed to be
\begin{eqnarray}
O \sim t^{\alpha} L_\parallel^{-1/2}, \label{eq:O}
\end{eqnarray}
where $\alpha$ is a phenomenological exponent to be determined  This, along with Eq  \eqref{eq:Oscalingass}, implies $\tilde f_O(x) \sim x^{\alpha} $ Comparing the finite-size behaviour in Eq ~\eqref{eq:O} with Eq ~\eqref{eq:Oscalingass} one actually infers,
\begin{eqnarray}
\alpha &=& \frac{1+ \Delta -2 \beta/\nu}{2 \, (4- \eta)}  \label{eq:alpha}
\end{eqnarray}
This equation, together with the hyperscaling relation $\Delta - 2 \beta/\nu= - \eta$ in two spatial dimensions, shows that the prediction $\alpha = 1/8$ of the Gaussian theory [see Eq  \eqref{eq:Ot}] can be obtained only when $\eta=0,$ which is the case for the IDLG (exactly) and the RDLG (approximately) but not for the LG  

On the other hand,  Eq ~\eqref{eq:alpha} predicts $\alpha = 1/10$ upon substituting the values of the critical exponents corresponding to the Ising  universality class (LG)



ground_truth: The generative interactive model used in the method is called the Coupled Generalized Dynamic Bayesian Network (C-GDBN).

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the dynamical behavior of the anisotropic order parameter following a quench to the critical point?

Read the following text and answer briefly.

Context 3:  This is consistent with the numerical simulation results presented in the main text, see Fig  \ref{fig:ising}(b) therein 

\begin{figure}[th]
\vspace*{0 2 cm}
 \centering
 \includegraphics[width=10 cm]{ /compare_binder pdf}

\caption{Comparison between the temporal evolution of the Binder cumulants $g$ corresponding to the $12^{th}$ transverse mode, $i e ,$ with $n_\perp =12,$ in the LG (lowest curve), IDLG and RDLG (two upper curves) on a $32 \times 32$ lattice  \label{fig:b}}
 \label{fig:binder}
\end{figure}


The emergence of this new value $1/10$ of the exponent $\alpha$ must be traced back to the non-Gaussian nature of higher fluctuating modes in the LG  In fact, even though the lowest mode behaves identically in all the three models we considered,  characterized by the same behaviour of $m$, higher modes show a significant difference in the non-driven case   


To illustrate this, we measured the Binder cumulants of higher modes which is defined  analogously to Eq ~(11), using transverse modes other than the first, i e , with $\mu=\tilde \sigma(0,2 \pi n_\bot/L_\bot)$ and $n_\bot>1 $  
 Figure \ref{fig:b} compares the same for all the three lattice gases for the mode with $n_\perp =12$ on a $32 \times 32$ lattice  Clearly, the curve corresponding to the LG (lowest, blue) departs from Gaussian behaviour $g=0$ (in practice, $e g ,$ $|g| \lesssim 0 005,$ corresponding to the shaded gray area) much earlier than it does for the IDLG  or RDLG (two upper curves, red and green respectively) 

Accordingly, the different dynamical behaviour of $O$, which involves a sum over all modes, can be attributed to the non-Gaussian nature of the higher modes in the LG  
Such a departure is not entirely surprising  In fact, for higher modes, mesoscopic descriptions such as the ones in Eqs  \eqref{eq:L-DLG} or \eqref{eq:g_evol} are not expected to hold, while the anisotropy at the microscopic level could be the mechanism leading to the Gaussianity of higher modes in the driven models 





ground_truth: It is well described by the Gaussian theory.