bluuebunny/crossref_metadata_2025 huggingface dataset:
A MICROBIOLOGICAL PERSPECTIVE ON OCULAR CONJUNCTIVITIS
Authors: Youvaraj Roshini , Kumaravel Santhosh Manikandan
Published: September 2024

Conjunctivitis is a condition that is often evident as inflammation of the conjunctiva commonly referred to as red eye or pink eye (AI-Mishhadani, 2020). Inflammation caused by this clinical condition can be characterized by cellular infiltration, exudation, and vascular dilation. In rare cases, chemosis and the accumulation of fluid are also seen. Conjunctivitis can be broadly classified as acute or chronic. Based on the microorganisms involved, they were also referred to as either infectious or non-infectious. The occurrence of the infections depends on the etiology, chronicity, severity, and degree of surrounding tissue. Mostly Viral and bacterial microorganisms are common factors, other factors like nutritional deprivation, immune-related syndromes, congenital metabolic syndromes, and other secondary ocular conditions like acute angle closure glaucoma, uveitis, endophthalmitis, carotid-cavernous fistula, anterior tumors and cellulitis cause conjunctivitis (Ali, 2023). Conjunctivitis is caused by various clinically important viral and bacterial microorganisms. Most of the conditions prevail due to allergic reactions. Type 1 allergies are responsible for most of the allergic conjunctivitis, and they are classified based on the occurrence of proliferative changes, dermatitis, and mechanical irritation by foreign bodies.
EPSTEIN BARR VIRUS (EBV)-ASSOCIATED CANCER BIOMARKERS FOR DIAGNOSIS, PROGNOSIS AND THERAPY: NARRATIVE REVIEW
Authors: Yaro Prof. Abubakar , Johnson Dr. Catherine , Bhattacharya Dr. Pranab Kumar
Published: September 2024

Oncoviruses are viruses that cause different cancers. To enable them survive, these viruses have evolved strategies that have direct or indirect carcinogenic effect by either encoding viral oncogenes which plays a role in the transformation of cells or causing persistent infection which results in chronic inflammation with significant tumorigenic effect. In most cases, virus do not directly initiate the Oncogenic process but plays a role in the acquisition of the risk factors that are linked with the development of cancer (Fig 1) over many years because the process of cancer development involves series of multiple steps consisting of process that are linked with several mutations due to genetic damage11,16 . Initiating of cancer by these oncoviruses is either via 1. Immune evasion where the cyclic GMP-AMP synthase associated stimulator of interferon gene (STING) , the retinoic acid-inducible gene 1 (RIG 1), and Toll-like receptor (TLR) pathways which are associated with immune responses through sensing of DNA and RNA viruses are inhibited16,17 ; 2. Abnormal regulation of cell cycle that target tumor protein 53 (p53) and retinoblastoma (pRB). These are tumour suppressor genes (TSG) are mostly found in tumour cases. These oncoviruses code for oncoproteins that have the ability of degrading or repressing p53 and pRB17, 18; and 3. Oncogenic viruses can also target series of host signalling pathways that controls cell growth and expansion; for e.g. mitogen-activated protein kinase (MAPK) pathway. In most cases, oncoviruses initially down regulates TSG or activate oncogenes that are associated with these pathways
VIRTUAL REALITY REVOLUTION: TRANSFORMING PEDIATRICS
Authors: Rathore Dr. Ashutosh Singh , Joshi Dr. Neelam
Published: September 2024

The article explores the transformative impact of Virtual Reality (VR) technology in pediatrics, focusing on its key components, applications, and implications for pediatric surgery. The VR system involves components such as Head-Mounted Displays, Sensors, Controllers, Computer Hardware, Audio Systems, and various software elements. The applications of VR in pediatrics extend to diverse domains like gaming, education, healthcare, and entertainment. Particularly, the article delves into the innovative use of VR in pediatric hospitals, providing distraction and relaxation for young patients, thereby enhancing their overall well-being. In the context of pediatric surgery, VR is discussed as a tool for preoperative planning, education, distraction, pain management, real-time visualization, collaboration, and recovery. The challenges and future trends of VR technology in pediatrics are also highlighted, encompassing safety concerns, content suitability, equipment comfort, cost, technical limitations, integration with healthcare systems, and ethical considerations. Despite challenges, the article concludes with optimism about the promising future of VR technology in pediatrics, anticipating advancements that will contribute to improved healthcare outcomes, enhanced patient experiences, and further developments in medical education and therapy.
CONTINUOUS GLUCOSE MONITORING : WHAT IS IT AND HOW DOES IT WORK?
Authors: Dubey Dr. Kinjalk , Verma Dr. Snehlata
Published: September 2024

Until recently, mainstay of blood glucose monitoring was mainly dependent on SMBG and HbA1c both of which may not serve as a measure of glycemic variability. Continuous glucose monitoring is a new method of measuring interstitial glucose levels on a continuous basis in an ambulatory individual. It consists of a sensor placed under the skin that measures interstitial glucose levels every few minutes all over the day, a software that compiles data into a single 24-hour period reading and a reader. CGM reduces the number of pinpricks, assesses glycemic variability and detects potentially dangerous complications like hypoglycaemia and helps in acute and long term therapy adjustments.
LIQUID BIOPSIES-A MULTIMODAL CANCER DIAGNOSTIC TOOL
Authors: Sonia Gon Dr (Prof).
Published: September 2024

Considering the challenges encountered in diagnostic methods related to conventional biopsies, a shift from traditional biopsies has been made possible through techniques such as liquid biopsy, empowering onco-pathologists with molecular profiling of tumour at all stage of its development. Liquid Biopsy targets comprises large or small molecules found in body fluids that lack cells or subcellular structures including proteins, nucleic acids, lipids, carbohydrates, small metabolites, and metal ions and targets with cellular or subcellular structures, such as single or clustered circulating tumor cells (CTCs), circulating cancer-related fibroblasts (CAF), immune cells, tumor-educated platelets (TEP), extracellular vesicles (EVs), and circulating mitochondria. These analytes can be assessed to gather information about both the overall tumor burden and the underlying biology, particularly as cancer cells undergo immunoediting and encounter evolutionary bottlenecks induced by therapeutic interventions. Pre-analytical variables may hamper the result of the analytes as the molecular characteristics of clinical samples can undergo significant alterations throughout the initial processing steps, encompassing everything from gathering the specimen to extracting the desired molecules like nucleic acids. Real time PCR, Digital PCR and Next Generation Sequencing are the tools by which these analytes can be analysed. Liquid biopsy testing has a highly attractive therapeutic use, but it is still confined to primary tumor identification, treatment response assessment, therapy monitoring, minimal residual disease detection, tumor heterogeneity characterization, and formation of resistances to targeted therapies.
ARTIFICIAL INTELLIGENCE IN PAEDIATRIC ANAESTHESIA
Authors: De Dr. Anisha , Sasikumar Dr. Gayatri
Published: September 2024

Artificial intelligence (AI) is currently the buzz word in health care and perioperative medicine. This chapter gives a brief outline of the various applications of AI in Paediatric Anaesthesia. Starting with understanding some basic concepts and terminology used in AI, it goes on to describe the advantage of machine learning and AI in anaesthesia. The scope of AI in various stages of our anaesthesia practice beginning from preoperative assessment, intraoperative management and post operative care, to predicting perioperative outcomes, guiding transfusion protocols and understanding pain in children has been explored. Other ancillary uses of AI such as paediatric critical care, clinical decision support systems, operating room logistics, education and skill development etc have also been investigated. Finally, it lays out the limitations of AI in anaesthesia practice.
Role of Artificial Intelligence in Education
Authors: Muhammad Athar Hussain  , Nazish Akhtar  , Sana Kiran  , Mehwish Noreen
Published: September 2024

This study was conducted to find out the role of Artificial Intelligence in education. The objectives of this study are: 1) To examine the significance of artificial intelligence in the field of education. 2) To determine the problems and possibilities of using artificial intelligence within the land of education, examining the relevant factors is important.  3) To explore the challenges of artificial intelligence inherent in the educational field. 4)  To examine the potential benefits of incorporating artificial intelligence in education. The population of this study is all colleges (government and private) in the district of Rahim Yar Khan. Of these 20 colleges, 400 students (boys and girls) and 150 teachers (males and females) participated as a sample. The study is descriptive, and the quantitative research method is utilized. Two self-structured questionnaires were used as a research tool: one for students, comprising 40 items, and one for teachers consisting of 30 items. A simple random sampling technique is used for data collection. The collected data was analyzed with the help of SPSS.  The results revealed that artificial intelligence plays a significant role in education and improves personalized learning experiences. AI technology is capable of fulfilling the needs of teachers and pupils in the teaching and learning process effectively e.g. tutoring, communication, evaluation, analysis, supervision, etc. It enhances the teaching and learning process by using modern technologies and methodologies. In short, the use of AI in education and learning is very noteworthy.
Diagnostic significance of determining products of DNA rearrangments of the T-and-B cell receptor TREC/KREC in common variable immunodeficiency
Authors: Polyakova E. A. , Guryanova I. E. , Sharapova S. O. , Sakovich I. S. , Shitikova M. G. , Kupchinskaya A. N. , Volodashchik Т. P. , Tsimokhava Y. V. , Aheyeu N. , Aleshkevich S. N. , Zharankova Yu. S. , Solntsava A. V. , Belevtsev M. V.
Published: September 2024

Common variable immunedeficiency (CVID) is a group of diseases that are inborn errors of the immune system and are characterized by impaired production of protective antibodies. The reason is a defect in the T- and B-cells, leading to impaired ability to produce specific antibodies after vaccination and infections with a significant decrease in immunoglobulins. Laboratory methods for diagnosing CVID usually include: flow cytometry and enzyme-linked immunosorbent assay to determine the levels of immunoglobulins (IgG, IgA, IgM) and antibody titer, however, these methods do not provide sufficient information about the neogenesis of lymphocytes. Our study is aimed at obtaining information about the possibility of using a simple and effective method for determining T- and B-lymphocyte receptor recombination products (TREC/KREC) in CVID. This method allows you to evaluate the neogenesis of T and B lymphocytes. The study included 12 patients diagnosed with CVID at the age of 11,2 (7,8; 15,0) years. In 2 patients CVID was determined by defects in the NFkB1 and NFkB2 genes. In 10 patients with CVID, the genetic defect was not identified; the diagnosis was established on the basis of clinical and laboratory data. To assess the diagnostic significance of the analyzed method, ROC analysis was used, followed by calculation of diagnostic sensitivity and specificity for each indicator. Our data allows us to assert that the quantitative determination of TREC/ KREC allows using this method with high diagnostic sensitivity and specificity at the stages of diagnosing CVID.
Review of herbal remedies in alternative antihypertensive and neuroprotective treatment of glaucoma
Authors: Nagornova Z. M. , Seleznev A. V. , Korelina V. E. , Kuroyedov A. V. , Gazizova I. R. , Razhko Yu. I. , Bulakh I. A.
Published: September 2024

Review of herbal remedies in alternative antihypertensive and neuroprotective treatment of glaucoma Due to the fact that glaucoma is a chronic, slowly progressive disease, patients are often disappointed in traditional treatment methods, and this leads to an independent search for other treatment strategies. The purpose of this review is to summarize data on the effect of herbal agents on the course of the glaucomatous process and discuss the validity of their use. An analysis of works devoted to the study of the neuroprotective and hypotensive effects of alternative medicine was carried out. The results presented in the review allow us to conclude that traditional treatment tactics remain relevant, and the prescription of any alternative agents requires special caution and does not eliminate the need for adequate control of intraocular pressure levels.
Assessment of the activity of remote gamma radiation sources
Authors: Nilova E. K. , Buzdalkin K. N. , Samsonov V. L.
Published: September 2024

A computer-oriented method for rapid assessment of the activity of remote gamma radiation sources in situ (in the field without sampling) is proposed. For calibration of portable and on-board detection units, reference gamma radiation sources are sequentially located at two points: one close to the crystal body, and the second, with an activity of at least 50 kBq, at a distance of 2 m or more along the axis of the detector. The net areas of the total absorption photopics, the live time of the spectrum set, the distances to the sources and their activity are used to determine special calibration coefficients. The calibration coefficients, together with the zero-distance efficiency curve, are used to assess the activity of remote gamma radiation sources (if the distance to the source exceeds its size by an order of magnitude or more). When calculating, the approximate distance to the detector is indicated, the material and wall thickness of the container can be taken into account. An independent expert examination found that the uncertainty of the proposed measurement method does not exceed 30% (p=0,95), which is quite acceptable for in-situ studies.
Post-COVID syndrome from the perspective of environmental psychiatry
Authors: Bronsky V. I. , Tolkanets S. V. , Bronskaya K. V. , Gavrilyuk Е. N.
Published: September 2024

126 outpatients were examined. In January-June 2023 – 29 people with post-Covid syndrome. In January-June 2022 – 47 people were anxious patients with signs of Covid phobia and 50 people with neuropsychiatric disorders who fell ill even before the COVID-19 pandemic. The study was conducted according to the methodology in environmental psychiatry using the author’s quantified map, including: socio-demographic, anamnestic sections, determination of the perception of socio-environmental factors, a clinical section with assessment of mental status according to ICD-10 and psychophysiological indicators – anxiety and vegetative support. What is common to all groups is that 2/3 of women have had a coronavirus infection, mostly in a mild form. As a result of the study, the predominantly psychogenic etiology of post-Covid syndrome was established, with leading anxiety spectrum disorders. Long-term exposure to anxiety causes organic transformation with an increase in cognitive dysfunction, cerebrasthenia and the formation of psychosomatic pathology. At the basis of cognitive dissonance, there is a tendency to reduce the perception of the danger of coronavirus infection, in the presence of signs of Covid phobia, which is the essence of the phenomenon. The phenomenon of decreased perception of the coronavirus infection factor affects the weakening of vaccine motivation. Taking into account clinical, personality-typological characteristics and peculiarities of perception of the environment provides grounds for targeted prevention, psychocorrection and rehabilitation.
Tendências futuras para a biodiversidade na florestação urbana de São Paulo, Brasil: insights para a década da restauração
Authors: Lino Raimunda Antônia , Ruiz Mauro Silva , Galhardo Cassiano , Nascimento Ana Paula Branco do , Ferreira Mauricio Lamano , Santos Mario Roberto dos
Published: September 2024

A cidade de São Paulo possui três viveiros municipais de distribuição de exemplares de plantas que atendem à demanda de seus projetos paisagísticos e o aumento da cobertura arbórea. Um deles (Manequinho Lopes) recebe mudas de árvores pelos processos de compensação ambiental contratados pela Secretaria Municipal do Verde e Meio Ambiente (SVMA). Este trabalho teve como objetivo avaliar o cenário da biodiversidade arbórea recebida entre julho de 2013 e julho de 2018 pelo viveiro Manequinho Lopes, como medida de compensação ambiental. Os resultados indicaram que 144.727 mudas de árvores foram recebidas pelo viveiro, com aproximadamente 80% do total pertencendo a apenas 30 espécies, sendo que metade delas pertencem a apenas 10 grupos diferentes. Encontramos apenas duas famílias predominantes: Myrtaceae e Bignoniaceae, evidenciando o futuro risco de homogeneização biótica. Em relação aos atributos ecológicos, constatou-se que 33% das espécies eram zoocóricas, 16% autocóricas e 22% anemocóricas. A maioria deles eram espécimes não ameaçados de extinção.
Rancang Bangun Aplikasi Profil Teknik Informatika Politeknik Kampar Menggunakan Sistem Operasi Android
Authors: Oktorina Fenty
Published: September 2024

In the digital era, people use smartphones almost all the time, showing that smartphones have become a part of human life. This phenomenon is used by many parties to promote quickly and practically. Likewise, the Informatics Engineering Study Program (PS-TIF) is considered necessary to create a profile that can be accessed via smartphones that use the Android operating system
Pembuatan Arang Aktif Dari Limbah Sekam Padi Sebagai Adsorben Dan Penyedia Unsur Hara
Authors: Fatmayati Fatmayati
Published: September 2024

Sources of raw materials that can be made into activated charcoal come from animals, plants, waste or minerals that contain carbon. In 2012 rice production was estimated at 68.59 million tons of GKG, an increase of 2.84 million tons (4.31 percent) compared to 2011. Based on the above conditions and the potential of rice husk as a raw material for activated charcoal, it is necessary to process rice husk so that it can be used as activated charcoal. The purpose of this study was to determine the processing of rice husk into activated charcoal and the characteristics of the activated charcoal produced and to determine the potential of charcoal as an adsorbent and nutrient provider. The method used in this study refers to SNI 06-3730-1995. The fixed variable was the activation process of rice husk with 0.5M NaOH at a temperature of 800C for 2 hours, while the changing variable was the temperature of 4000C and 5000C with carbonization times of 30,45,60,75,90,105 and 120 minutes
Perbandingan Sistem Kendali Pid Dan Kendali Lqr Pada Sistem Suspensi Aktif Bus (1/4) Menggunakan Simulasi Matlab
Authors: Ridwan Muhammad
Published: September 2024

A vehicle suspension system must be able to isolate or reduce the vibration of vehicle body due to unevenness of the road surface. To solve the situation as above, it was needed a controller on the actuator (active suspension) to dampen oscillations of body. In this study, it was designed a controller at a quarter of the suspension system bus using control LQR (Linear Quadratic Regulator) and compared it with PID control. This system will be modeled by State Space and Transfer Function models using Matlab 2011. The results obtained were LQR control system was better than the PID. In LQR, the value of ? was 0.1 and in PID, the value of gain is Kp = 832 100, Ki = 624 075 and 208 025 on the Kd = PID. LQR controller slower reach steady state compared with PID controllers. Stable conditions will be achieved within 30 seconds before the control and after using controller, time of stability to be 3 seconds.
Perancangan Perawatan Mesin Cetak Offset Dengan Pendekatan RCM, (Reliability Centered Maintenance)
Authors: Apif Sofyan  , Indah Wahyu Utami  , Ringgo Ismoyo Buwono
Published: September 2024

Machines play a crucial role in a production process, highlighting the need for maintenance to ensure their proper functioning. The methods employed include Fault Tree Analysis (FTA), Failure Mode and Effect Analysis (FMEA), and distribution determination. The repair times for each CMYK component are as follows: the bearing component requires 93.541 hours or 4 days, Griver needs 163.235 hours or 7 days, the seal requires 195.349 hours or 9 days, the linner pen needs 248.803 hours or 10 days, and the ink tank needs 260.123 hours or 11 days.
Marketing Mix Untuk Meningkatkan Penjualan Produk Pada Toko Gitar Dimdim Musik Di Baki Sukoharjo
Authors: Ridwan Raja Refo  , Indah Wahyu Utami  , Brillian Nur Diansari
Published: September 2024

In the current era, the development of the creative music industry in Indonesia is so fast where competition between the creative music industries is getting tougher every day. This does not only apply to large companies, Micro, Small and Medium Enterprises (MSMEs) but also participating in the competition. This study aims to apply the marketing mix to increase sales of Dimdim Musik guitar products in Baki, Sukoharjo. The results of this study are that there are 2 influential variables, namely price variables, promotion variables and 5 variables that not affect product sales, namely place variables, people variables, product variabels, process variabel, physical evidence variabel.
Perancangan Ulang Mesin Spot Welding Menggunakan Metode Benchmarking (Studi Kasus: Bengkel Fabrikasi Logam Dan Manufaktur SMK Negeri 2 Surakarta)
Authors: Ismail Hakim Asy Syidiq  , Febrina Agusti  , Ringgo Ismoyo Buwono
Published: September 2024

Spot welding is used as a tool to meet the UKK (Skill Competency Test) requirements in the Metal Fabrication and Manufacturing Engineering department at SMK Negeri 2 Surakarta in the form of welding workpieces from iron plates. The results of the welding are non-sticky and perforated iron plates. This research aims to redesign the spot welding machine by adding a TDR (Time Delay Relay) component to regulate the welding time using the benchmarking method. Data collection through interviews and observation. The results of the benchmarking analysis show that spot welding has easier welding specifications, has TDR and automatic switch components, dimensions of 45 x 23 x 15 cm and is capable of welding up to a plate thickness of 1,5 + 1,5 mm. Has a selling price of Rp. 1,200,000,-, so that it is able to compete in the market.
Perancangan Alat Pengering Jagung Tipe Bed Dryer Dengan Metode VDI 2221
Authors: Sholikhin Tri Admojo  , Ferida Yuamita
Published: September 2024

The Budi Bakti Masa Farmer Group is a farmer group in Sumberrejo Village, Tempel District, Sleman Regency, DIY. When entering the corn harvest season, farmers dry their crops with the help of sunlight. The process of drying corn is done by drying it in direct sunlight. During the rainy season, farmers find it difficult to dry their corn crops. Corn drying during the rainy season  take 3-5 days or even more. The purpose of this research is to design a corn dryer that can speed up the drying process and is not dependent on the weather. The research was conducted using the Verein Deutscher Ingenieure (VDI) 2221 method. Data was collected using a questionnaire. The questionnaire used in this regard is an open and closed questionnaire. The respondents in this study were members of the Budi Bakti Masa farmer group, a total of 21 people. In designing the VDI 2221 method, there are 4 stages, namely job description, concept planning, form design, and detailed design. Based on the trial results, the corn dryer was able to dry 100 kg of rice with a moisture content of 36.3% to dry rice with a moisture content of 12% within 6 hours.
Connecting Elliptic Curves with Finite Fields
Authors: Kun Jeremy
Published: September 2024

So here we are. We’ve studied the general properties of elliptic curves, written a program for elliptic curve arithmetic over the rational numbers, and taken a long detour to get some familiarity with finite fields (the mathematical background and a program that implements arbitrary finite field arithmetic). And now we want to get back on track and hook our elliptic curve program up with our finite field program to make everything work.
Trees—A Primer
Authors: Kun Jeremy
Published: September 2024

This post comes in preparation for a post on decision trees (a specific type of tree used for classification in machine learning). While most mathematicians and programmers are familiar with trees, we have yet to discuss them on this blog. For completeness, we’ll give a brief overview of the terminology and constructions associated with trees, and describe a few common algorithms on trees.
Miller-Rabin Primality Test
Authors: Kun Jeremy
Published: September 2024

Problem: Determine if a number is prime, with an acceptably small error rate.
Concrete Examples of Quantum Gates
Authors: Kun Jeremy
Published: September 2024

So far in this series we’ve seen a lot of motivation and defined basic ideas of what a quantum circuit is. But on rereading my posts, I think we would all benefit from some concreteness. “Local” operations So by now we’ve understood that quantum circuits consist of a sequence of gates $ A_1, \dots, A_k$, where each $ A_i$ is an 8-by-8 matrix that operates “locally” on some choice of three (or fewer) qubits.
Introducing Elliptic Curves
Authors: Kun Jeremy
Published: September 2024

With all the recent revelations of government spying and backdoors into cryptographic standards, I am starting to disagree with the argument that you should never roll your own cryptography. Of course there are massive pitfalls and very few people actually need home-brewed cryptography, but history has made it clear that blindly accepting the word of the experts is not an acceptable course of action.
Universal Properties
Authors: Kun Jeremy
Published: September 2024

Previously in this series we’ve seen the definition of a category and a bunch of examples, basic properties of morphisms, and a first look at how to represent categories as types in ML. In this post we’ll expand these ideas and introduce the notion of a universal property. We’ll see examples from mathematics and write some programs which simultaneously prove certain objects have universal properties and construct the morphisms involved.
Stable Marriages and Designing Markets
Authors: Kun Jeremy
Published: September 2024

Here is a fun puzzle. Suppose we have a group of 10 men and 10 women, and each of the men has sorted the women in order of their preference for marriage (that is, a man prefers to marry a woman earlier in his list over a woman later in the list). Likewise, each of the women has sorted the men in order of marriageability. We might ask if there is any way that we, the omniscient cupids of love, can decide who should marry to make everyone happy.
Voltage, Temperature, and Harmonic Functions
Authors: Kun Jeremy
Published: September 2024

This is a guest post by my friend and colleague Samantha Davies. Samantha is a math Ph.D student at the University of Washington, and a newly minted math blogger. Go check out her blog, With High Probability. If I said “let’s talk about temperature and voltage”, you might be interested, but few would react the same if instead I suggested an umbrella term: harmonic functions.
Methods of Proof — Diagonalization
Authors: Kun Jeremy
Published: September 2024

A while back we featured a post about why learning mathematics can be hard for programmers, and I claimed a major issue was not understanding the basic methods of proof (the lingua franca between intuition and rigorous mathematics). I boiled these down to the “basic four,” direct implication, contrapositive, contradiction, and induction. But in mathematics there is an ever growing supply of proof methods.
Linear Regression
Authors: Kun Jeremy
Published: September 2024

Machine learning is broadly split into two camps, statistical learning and non-statistical learning. The latter we’ve started to get a good picture of on this blog; we approached Perceptrons, decision trees, and neural networks from a non-statistical perspective. And generally “statistical” learning is just that, a perspective.
Cauchy-Schwarz Inequality (and Amplification)
Authors: Kun Jeremy
Published: September 2024

Problem: Prove that for vectors $ v, w$ in an inner product space, the inequality $$\displaystyle |\left \langle v, w \right \rangle | \leq \ v \ \ w \$$ Solution: There is an elementary proof of the Cauchy-Schwarz inequality (see the Wikipedia article), and this proof is essentially the same. What makes this proof stand out is its insightful technique, which I first read about on Terry Tao’s blog.
Fixing Bugs in "Computing Homology"
Authors: Kun Jeremy
Published: September 2024

A few awesome readers have posted comments in Computing Homology to the effect of, “Your code is not quite correct!” And they’re right! Despite the almost year since that post’s publication, I haven’t bothered to test it for more complicated simplicial complexes, or even the basic edge cases! When I posted it the mathematics just felt so solid to me that it had to be right (the irony is rich, I know).
A Spectral Analysis of Moore Graphs
Authors: Kun Jeremy
Published: September 2024

For fixed integers $ r > 0$, and odd $ g$, a Moore graph is an $ r$-regular graph of girth $ g$ which has the minimum number of vertices $ n$ among all such graphs with the same regularity and girth.
The Inequality
Authors: Kun Jeremy
Published: September 2024

Math and computer science are full of inequalities, but there is one that shows up more often in my work than any other. Of course, I’m talking about $$\displaystyle 1+x \leq e^{x}$$ This is The Inequality. I’ve been told on many occasions that the entire field of machine learning reduces to The Inequality combined with the Chernoff bound (which is proved using The Inequality). Why does it show up so often in machine learning?
Conditional (Partitioned) Probability — A Primer
Authors: Kun Jeremy
Published: September 2024

One of the main areas of difficulty in elementary probability, and one that requires the highest levels of scrutiny and rigor, is conditional probability. The ideas are simple enough: that we assign probabilities relative to the occurrence of some event. But shrewd applications of conditional probability (and in particular, efficient ways to compute conditional probability) are key to successful applications of this subject.
Zero-Knowledge: Definitions and Theory
Authors: Kun Jeremy
Published: September 2024

The next Monday, when the fathers were all back at work, we kids were playing in a field. One kid says to me, “See that bird? What kind of bird is that?” I said, “I haven’t the slightest idea what kind of a bird it is.” He says, “It’s a brown-throated thrush. Your father doesn’t teach you anything!” But it was the opposite. He had already taught me: “See that bird?
Methods of Proof — Direct Implication
Authors: Kun Jeremy
Published: September 2024

I recently posted an exploratory piece on why programmers who are genuinely interested in improving their mathematical skills can quickly lose stamina or be deterred. My argument was essentially that they don’t focus enough on mastering the basic methods of proof before attempting to read research papers that assume such knowledge.
Homology Theory — A Primer
Authors: Kun Jeremy
Published: September 2024

This series on topology has been long and hard, but we’re are quickly approaching the topics where we can actually write programs.
Sending and Authenticating Messages with Elliptic Curves
Authors: Kun Jeremy
Published: September 2024

Last time we saw the Diffie-Hellman key exchange protocol, and discussed the discrete logarithm problem and the related Diffie-Hellman problem, which form the foundation for the security of most protocols that use elliptic curves. Let’s continue our journey to investigate some more protocols. Just as a reminder, the Python implementations of these protocols are not at all meant for practical use, but for learning purposes.
My Graduate Career in Math
Authors: Kun Jeremy
Published: September 2024

2010–2011 (Year 0) I had just switched my major at Cal Poly State University from computer science to math. I wanted to double major but California was in a budget crisis and a few weeks before I tried submitting my double-major request the Provost for the CSU system put a blanket ban on double majors.
One definition of algorithmic fairness: statistical parity
Authors: Kun Jeremy
Published: September 2024

If you haven’t read the first post on fairness, I suggest you go back and read it because it motivates why we’re talking about fairness for algorithms in the first place. In this post I’ll describe one of the existing mathematical definitions of “fairness,” its origin, and discuss its strengths and shortcomings.
Zero Knowledge Proofs — A Primer
Authors: Kun Jeremy
Published: September 2024

In this post we’ll get a strong taste for zero knowledge proofs by exploring the graph isomorphism problem in detail. In the next post, we’ll see how this relates to cryptography and the bigger picture. The goal of this post is to get a strong understanding of the terms “prover,” “verifier,” and “simulator,” and “zero knowledge” in the context of a specific zero-knowledge proof.
Weak Learning, Boosting, and the AdaBoost algorithm
Authors: Kun Jeremy
Published: September 2024

When addressing the question of what it means for an algorithm to learn, one can imagine many different models, and there are quite a few. This invariably raises the question of which models are “the same” and which are “different,” along with a precise description of how we’re comparing models.
The Reasonable Effectiveness of the Multiplicative Weights Update Algorithm
Authors: Kun Jeremy
Published: September 2024

papad Hard to believe Sanjeev Arora and his coauthors consider it “a basic tool [that should be] taught to all algorithms students together with divide-and-conquer, dynamic programming, and random sampling.” Christos Papadimitriou calls it “so hard to believe that it has been discovered five times and forgotten.” It has formed the basis of algorithms in machine learning, optimization, game theory, economics, biology, and more.
The Fundamental Group — A Primer
Authors: Kun Jeremy
Published: September 2024

Being part of the subject of algebraic topology, this post assumes the reader has read our previous primers on both topology and group theory. As a warning to the reader, it is more advanced than most of the math presented on this blog, and it is woefully incomplete. Nevertheless, the aim is to provide a high level picture of the field with a peek at the details.
The Many Faces of Set Cover
Authors: Kun Jeremy
Published: September 2024

A while back Peter Norvig posted a wonderful pair of articles about regex golf. The idea behind regex golf is to come up with the shortest possible regular expression that matches one given list of strings, but not the other. “Regex Golf,” by Randall Munroe. In the first article, Norvig runs a basic algorithm to recreate and improve the results from the comic, and in the second he beefs it up with some improved search heuristics.
Categories, What's the Point?
Authors: Kun Jeremy
Published: September 2024

Perhaps primarily due to the prominence of monads in the Haskell programming language, programmers are often curious about category theory. Proponents of Haskell and other functional languages can put category-theoretic concepts on a pedestal or in a mexican restaurant, and their benefits can seem as mysterious as they are magical. For instance, the most common use of a monad in Haskell is to simulate the mutation of immutable data.
The Codes of Solomon, Reed, and Muller
Authors: Kun Jeremy
Published: September 2024

Last time we defined the Hamming code. We also saw that it meets the Hamming bound, which is a measure of how densely a code can be packed inside an ambient space and still maintain a given distance. This time we’ll define the Reed-Solomon code which optimizes a different bound called the Singleton bound, and then generalize them to a larger class of codes called Reed-Muller codes.
Adversarial Bandits and the Exp3 Algorithm
Authors: Kun Jeremy
Published: September 2024

In the last twenty years there has been a lot of research in a subfield of machine learning called Bandit Learning. The name comes from the problem of being faced with a large sequence of slot machines (once called one-armed bandits) each with a potentially different payout scheme.
Introducing Categories
Authors: Kun Jeremy
Published: September 2024

For a list of all the posts on Category Theory, see the Main Content page. It is time for us to formally define what a category is, to see a wealth of examples. In our next post we’ll see how the definitions laid out here translate to programming constructs. As we’ve said in our soft motivational post on categories, the point of category theory is to organize mathematical structures across various disciplines into a unified language.
Singular Value Decomposition Part 2: Theorem, Proof, Algorithm
Authors: Kun Jeremy
Published: September 2024

I’m just going to jump right into the definitions and rigor, so if you haven’t read the previous post motivating the singular value decomposition, go back and do that first. This post will be theorem, proof, algorithm, data. The data set we test on is a thousand-story CNN news data set. All of the data, code, and examples used in this post is in a github repository, as usual. We start with the best-approximating $ k$-dimensional linear subspace.
Tensorphobia and the Outer Product
Authors: Kun Jeremy
Published: September 2024

Variations on a theme Back in 2014 I wrote a post called How to Conquer Tensorphobia that should end up on Math $ \cap$ Programming’s “greatest hits” album. One aspect of tensors I neglected to discuss was the connection between the modern views of tensors and the practical views of linear algebra. I feel I need to write this because every year or two I forget why it makes sense.
A Rook Game
Authors: Kun Jeremy
Published: September 2024

Problem: Two players take turns moving a rook on an 8×8 chessboard. The rook is only allowed to move south or west (but not both in a single turn), and may move any number of squares in the chosen direction on a turn. The loser is the player who first cannot move the rook. What is the optimal play for any starting position? rook-board Solution: Take advantage of the symmetry of the board.
Constructing Topological Spaces — A Primer
Authors: Kun Jeremy
Published: September 2024

Last time we investigated the (very unintuitive) concept of a topological space as a set of “points” endowed with a description of which subsets are open. Now in order to actually arrive at a discussion of interesting and useful topological spaces, we need to be able to take simple topological spaces and build them up into more complex ones.
On Coloring Resilient Graphs
Authors: Kun Jeremy
Published: September 2024

I’m pleased to announce that another paper of mine is finished. This one just got accepted to MFCS 2014, which is being held in Budapest this year (this whole research thing is exciting!). This is joint work with my advisor, Lev Reyzin. As with my first paper, I’d like to explain things here on my blog a bit more informally than a scholarly article allows.
Elliptic Curves as Python Objects
Authors: Kun Jeremy
Published: September 2024

Last time we saw a geometric version of the algorithm to add points on elliptic curves. We went quite deep into the formal setting for it (projective space $ \mathbb{P}^2$), and we spent a lot of time talking about the right way to define the “zero” object in our elliptic curve so that our issues with vertical lines would disappear.
The Two-Dimensional Fourier Transform and Digital Watermarking
Authors: Kun Jeremy
Published: September 2024

We’ve studied the Fourier transform quite a bit on this blog: with four primers and the Fast Fourier Transform algorithm under our belt, it’s about time we opened up our eyes to higher dimensions. Indeed, in the decades since Cooley &
Properties of Morphisms
Authors: Kun Jeremy
Published: September 2024

This post is mainly mathematical. We left it out of our introduction to categories for brevity, but we should lay these definitions down and some examples before continuing on to universal properties and doing more computation. The reader should feel free to skip this post and return to it later when the words “isomorphism,” “monomorphism,” and “epimorphism” come up again.
Infinitely Many Primes (Using Topology)
Authors: Kun Jeremy
Published: September 2024

Problem: Prove there are infinitely many prime numbers. Solution: First recall that an arithmetic progression with difference $ d$ is a sequence of integers $ a_n \subset \mathbb{Z}$ so that for every pair $ a_k, a_{k+1}$ the difference $ a_{k+1} – a_k = d$. We proceed be defining a topology on the set of integers by defining a basis $ B$ of unbounded (in both directions) arithmetic progressions.
Groups — A Primer
Authors: Kun Jeremy
Published: September 2024

The study of groups is often one’s first foray into advanced mathematics. In the naivete of set theory one develops tools for describing basic objects, and through a first run at analysis one develops a certain dexterity for manipulating symbols and definitions. But it is not until the study of groups that one must step back and inspect the larger picture.
Topological Spaces — A Primer
Authors: Kun Jeremy
Published: September 2024

In our last primer we looked at a number of interesting examples of metric spaces, that is, spaces in which we can compute distance in a reasonable way. Our goal for this post is to relax this assumption. That is, we want to study the geometric structure of space without the ability to define distance.
(Finite) Fields — A Primer
Authors: Kun Jeremy
Published: September 2024

So far on this blog we’ve given some introductory notes on a few kinds of algebraic structures in mathematics (most notably groups and rings, but also monoids). Fields are the next natural step in the progression. If the reader is comfortable with rings, then a field is extremely simple to describe: they’re just commutative rings with 0 and 1, where every nonzero element has a multiplicative inverse.
Formulating the Support Vector Machine Optimization Problem
Authors: Kun Jeremy
Published: September 2024

The hypothesis and the setup This blog post has an interactive demo (mostly used toward the end of the post). The source for this demo is available in a Github repository. Last time we saw how the inner product of two vectors gives rise to a decision rule: if $ w$ is the normal to a line (or hyperplane) $ L$, the sign of the inner product $ \langle x, w \rangle$ tells you whether $ x$ is on the same side of $ L$ as $ w$.
Seam Carving for Content-Aware Image Scaling
Authors: Kun Jeremy
Published: September 2024

The Problem with Cropping Every programmer or graphic designer with some web development experience can attest to the fact that finding good images that have an exactly specified size is a pain. Since the dimensions of the sought picture are usually inflexible, an uncomfortable compromise can come in the form of cropping a large image down to size or scaling the image to have appropriate dimensions. Both of these solutions are undesirable.
Decision Trees and Political Party Classification
Authors: Kun Jeremy
Published: September 2024

Last time we investigated the k-nearest-neighbors algorithm and the underlying idea that one can learn a classification rule by copying the known classification of nearby data points. This required that we view our data as sitting inside a metric space; that is, we imposed a kind of geometric structure on our data. One glaring problem is that there may be no reasonable way to do this.
Functoriality
Authors: Kun Jeremy
Published: September 2024

Last time we worked through some basic examples of universal properties, specifically singling out quotients, products, and coproducts. There are many many more universal properties that we will mention as we encounter them, but there is one crucial topic in category theory that we have only hinted at: functoriality. As we’ve repeatedly stressed, the meat of category theory is in the morphisms.
A Motivation for Quantum Computing
Authors: Kun Jeremy
Published: September 2024

Quantum mechanics is one of the leading scientific theories describing the rules that govern the universe. It’s discovery and formulation was one of the most important revolutions in the history of mankind, contributing in no small part to the invention of the transistor and the laser. Here at Math ∩ Programming we don’t put too much emphasis on physics or engineering, so it might seem curious to study quantum physics.
An Update on "Coloring Resilient Graphs"
Authors: Kun Jeremy
Published: September 2024

A while back I announced a preprint of a paper on coloring graphs with certain resilience properties. I’m pleased to announce that it’s been accepted to the Mathematical Foundations of Computer Science 2014, which is being held in Budapest this year. Since we first published the preprint we’ve actually proved some additional results about resilience, and so I’ll expand some of the details here.
Categories as Types
Authors: Kun Jeremy
Published: September 2024

In this post we’ll get a quick look at two ways to define a category as a type in ML. The first way will be completely trivial: we’ll just write it as a tuple of functions. The second will involve the terribly-named “functor” expression in ML, which allows one to give a bit more structure on data types. The reader unfamiliar with the ML programming language should consult our earlier primer.
Anti-Coordination Games and Stable Graph Colorings
Authors: Kun Jeremy
Published: September 2024

My First Paper I’m pleased to announce that my first paper, titled “Anti-Coordination Games and Stable Colorings,” has been accepted for publication! The venue is the Symposium on Algorithmic Game Theory, which will take place in Aachen, Germany this October.
Simulating a Biased Coin with a Fair Coin
Authors: Kun Jeremy
Published: September 2024

This is a guest post by my friend and colleague Adam Lelkes. Adam’s interests are in algebra and theoretical computer science. This gem came up because Adam gave a talk on probabilistic computation in which he discussed this technique. Problem: simulate a biased coin using a fair coin.
A Quasipolynomial Time Algorithm for Graph Isomorphism: The Details
Authors: Kun Jeremy
Published: September 2024

Update 2017-01-09: Laci claims to have found a workaround to the previously posted error, and the claim is again quasipolynoimal time! Updated arXiv paper to follow. Update 2017-01-04: Laci has posted an update on his paper. The short version is that one small step of his analysis was not quite correct, and the result is that his algorithm is sub-exponential, but not quasipolynomial time.
Multiple Qubits and the Quantum Circuit
Authors: Kun Jeremy
Published: September 2024

Last time we left off with the tantalizing question: how do you do a quantum “AND” operation on two qubits? In this post we’ll see why the tensor product is the natural mathematical way to represent the joint state of multiple qubits. Then we’ll define some basic quantum gates, and present the definition of a quantum circuit.
The Quantum Bit
Authors: Kun Jeremy
Published: September 2024

The best place to start our journey through quantum computing is to recall how classical computing works and try to extend it. Since our final quantum computing model will be a circuit model, we should informally discuss circuits first. A circuit has three parts: the “inputs,” which are bits (either zero or one); the “gates,” which represent the lowest-level computations we perform on bits;