Miracle-dz/UniFAR-FTUs huggingface dataset:
A Nearly-Optimal Bound for Fast Regression with 𝓁∞ Guarantee

Given a matrix $A\in \mathbb{R}^{n\times d}$ and a vector $b\in \mathbb{R}^n$, we consider the regression problem with $\ell_\infty$ guarantees: finding a vector $x'\in \mathbb{R}^d$ such that $ \|x'-x^*\|_\infty \leq \frac{\epsilon}{\sqrt{d}}\cdot \|Ax^*-b\|_2\cdot \|A^\dagger\|$ where $x^*=\arg\min_{x\in \mathbb{R}^d}\|Ax-b\|_2$. One popular approach for solving such $\ell_2$ regression problem is via sketching: picking a structured random matrix $S\in \mathbb{R}^{m\times n}$ with $m\ll n$ and $SA$ can be quickly computed, solve the ``sketched'' regression problem $\arg\min_{x\in \mathbb{R}^d} \|SAx-Sb\|_2$. In this paper, we show that in order to obtain such $\ell_\infty$ guarantee for $\ell_2$ regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with $m=\epsilon^{-2}d\log^3(n/\delta)$ such that solving the sketched regression problem gives the $\ell_\infty$ guarantee, with probability at least $1-\delta$. Moreover, the matrix $SA$ can be computed in time $O(nd\log n)$. Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in $d$ rows, $m=\Omega(\epsilon^{-2}d^{1+\gamma})$ for $\gamma=\Theta(\sqrt{\frac{\log\log n}{\log d}})$ is required. We also develop a novel analytical framework for $\ell_\infty$ guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.
Diagnostik und Behandlung physischer Frailty

Abstract Physical frailty is a physiological syndrome of older people. It is characterized by a reduced reserve, a reduced stressor resistance, and vulnerability to negative health outcomes. The assessment of physical frailty is increasingly applied to identify high risk patients prior to medical or surgical interventions. The present article describes Fried’s frailty phenotype, which is the most frequently applied diagnostic instrument of physical frailty, together with evidence based treatment options.
Defining fractals in a probability space

In [1] Billingsley defined Hausdorff dimension for subsets of a probability space, and developed relations with entropy and information theory. In [2] he explored the effect of varying the probability measure in the definition. In revisiting his work we will sharpen his density theorems so that they give results for measures as well as dimension (Lemmas 5.1 and 5.2). In Euclidean space R there is no generally accepted definition of a fractal, even though fractal sets are widely used as models for many physical phenomena. The idea behind these models is that of self-similarity or affineness which is based on the linear structure of Rd. These and other geometrical notions have no obvious meaning in an abstract probability space. One of us [11] proposed a measure-theoretic definition for subsets E c Rd: E should be called a fractal if
The Application of Linear Algebra Algorithm in the Production of Linear Matrix Inequalities

Discusses the theory and symbolic of the algorithm gives another potential application, but also in the system and control. For example, for the question, has made with special structure, but LMI problem data, may cause factorizations LMI more compact. One can even imagine using the algorithm around, looking for the opportunity to LMI automatic eliminate variables, so simplify problem solving, before they get a lot of influence and a potential solutions. We describe theory, the algorithm can be used to factor in the non commuting variable polynomial matrix and application system switches and control problem into a linear matrix inequality.
GREEN-SCHWARZ ACTION AND LOOP CALCULATIONS FOR SUPERSTRING

We argue that the Green-Schwarz explicitly 10d supersymmetric and 2d covariant approach without spin 1/2 and 3/2 fields on the world sheet may appear suitable for calculations of loops in superstring theory. We show how the cancellation of the Polyakov anomaly is realized, and the answer for the l-loop 4-point amplitudes is reproduced.
Electron mobility enhancement in strained-germanium n-channel metal-oxide-semiconductor field-effect transistors

The dependence of electron mobility on strain, channel direction, and substrate orientation is theoretically studied for the germanium n-channel metal-oxide-semiconductor field-effect transistors. For the unstrained channel, (111) substrate can provide the highest mobility among the three orientations, mainly due to its largest quantization mass and smallest conductivity mass in L valley. The tensile strain parallel to the [1¯10] channel direction on (111) substrate gives 4.1 times mobility of Si at 1MV∕cm, and the mobility enhancement starts to saturate for the strain larger than 0.5%. The compressive strain of ∼1.5% transverse to [1¯10] on (111) substrate yields 2.9 times mobility enhancement at 1MV∕cm.
Kommunikation zwischen Apothekern und Ärzten bei potenziell schweren Arzneimittelinteraktionen

Zusammenfassung Hintergrund Potenziell schwere Arzneimittelinteraktionen werden häufig durch Apotheker entdeckt. In solchen Fällen ist eine schnelle Kommunikation mit dem verschreibenden Arzt notwendig. Aufgrund der schwierigen telefonischen Erreichbarkeit wurde in einem vorausgegangenen Projekt eine Faxvorlage zur Meldung potenziell schwerer Arzneimittelinteraktionen entwickelt. In dieser Beobachtungsstudie wurden Häufigkeit und Art der gemeldeten Interaktionen evaluiert. Methoden Die Faxvorlage wurde Hausärzten und Apothekern im Bundesland Bremen vorgestellt. Die Schwere der Interaktionen wurde anhand der ABDA-Klassifikation (von 1: „schwerwiegende Folgen wahrscheinlich – kontraindiziert“ bis 8: „keine weiteren Maßnahmen erforderlich“) bestimmt. Teilnehmende Apotheker wurden gebeten, ein anonymisiertes Duplikat jeder Faxvorlage zur Verfügung zu stellen. Die interagierenden Arzneimittel, die Schweregrade der Interaktionen, Empfehlungen der Apotheker und die Rückantwort der Ärzte wurden deskriptiv ausgewertet. Ergebnisse 123 Faxe von 23 teilnehmenden Apotheken (1 – 25 Faxe/Apotheke) wurden ausgewertet. Bei 108 von 123 wurde eine Interaktion unterschiedlichen Schweregrades nach ABDA gemeldet. In den übrigen Fällen konnte der Schweregrad nicht ermittelt werden (n = 7) oder es handelte sich um eine Doppelmedikation (n = 8). Eine Rückantwort des Arztes war bei 69,4 % (n = 75) vorhanden. In Anlehnung an die Empfehlung der Apotheke wurde von den Ärzten ein alternatives Medikament verschrieben, die Medikation vorläufig/dauerhaft abgesetzt oder eine engmaschige Überwachung angeordnet (n = 23). Weiterhin wurde eine andere Therapieoption gewählt (n = 15) oder das Problem als bekannt eingestuft und die Verordnung beibehalten (31,5 %, n = 34). Eine Rücksprache mit dem Patienten wurde kaum angestrebt (n = 3). Diskussion Die Faxvorlage scheint bei Apothekern ein akzeptiertes Instrument zur Meldung potenziell schwerer Arzneimittelinteraktionen zu sein. Es kann mit wenig Aufwand zu einer Verbesserung der Arzneimitteltherapie beitragen. Entgegen der Intention meldeten Apotheker auch weniger schwere Arzneimittelinteraktionen. Hier ist auf das Risiko von zu vielen Warnhinweisen („over-alerting“) hinzuweisen, die zu einer unbeabsichtigten Vernachlässigung von ernsten Fällen führen können.
The 3-D Distribution of Abell Clusters

The Struble & Rood catalogue of all measured Abell cluster redshifts is analysed, with correction for the redshift incompleteness in the D = 5 − 6 subsamples, and clear evidence is found for selection effects in the Abell catalogue. When these are compensated for, a much reduced cluster correlation amplitude is indicated, with $${\xi _{cc}}(r) \approx {\left( {{r \over {14{\rm{ }}{h^{ - 1}}Mpc}}} \right)^{ - 1.8}},$$ and an upper limit ~ 800 km/s is placed on cluster peculiar velocities.
Primär- und Sekundärprävention des Multiplen Myeloms

Abstract Lifestyle factors such as diet, physical activity and exposure to noxious agents are modifiable factors that have a significant impact on the state of health and life expectancy of humans. The following article is intended to provide an overview of current knowledge on the influence of these lifestyle factors on the development and progression of multiple myeloma and is dedicated to the question of the extent to which prevention strategies can be usefully applied.
Comparison of Three Eradication Treatment Protocols for Pseudomonas Aeruginosa in Children and Adolescents with Cystic Fibrosis

Abstract Background Pseudomonas aeruginosa (Pa) continues to affect disease progression in cystic fibrosis (CF). However, the best eradication regimen remains unclear. This work compares three different antibiotic eradication regimens in pediatric CF: an administration according to a standard-operating procedure (SOP) order vs. administration outside of this order (ooSOP). Methods This observational study includes all CF patients<18 years who received one of three Pa eradication treatments in the past eight years at our center: 1) inhaled high-dose tobramycin (Hi-TOBI), 2) inhaled colistin+oral ciprofloxacin (COL/Cip), 3) inhaled low-dose tobramycin+4 intravenous 14-day Pa active antibiotic treatments (lo-Tobra/IV). We compared eradication rates of the three treatment regimens performed according to the SOP-based order vs. ooSOP. Logistic regression analysis was performed to identify risk factors for eradication failure. Results Performed according to SOP order, Hi-TOBI showed the greatest efficacy, followed by lo-Tobra/IV and finally COL/Cip, while ooSOP lo-Tobra/IV was most successful, followed by COL/Cip and Hi-TOBI. Previous Pa-infections and Pa-therapies along with age at CF diagnosis were risk factors for eradication failure. Conclusion Antibiotic treatment in SOP-based pre-defined order leads to significantly better eradication rates than individual modifications of the order of administration. A short course of inhalational high-dose Tobramycin is most successful at the first attempt. Prolonged antibiotic therapy seems to improve eradication after failed initial attempts.
Linear and Nonlinear Multivariable Feedback Control: A Classical Approach

Preface. Part I Linear Multivariable Control System. 1 Canonical representations and stability analysis of linear MIMO systems. 1.1 Introduction. 1.2 General linear square MIMO systems. 1.3 Uniform MIMO systems. 1.4 Normal MIMO systems. 1.5 Multivariable root loci. 2 Performance and design of linear MIMO systems. 2.1 Introduction. 2.2 Generalized frequency response characteristics and accuracy of linear MIMO systems under sinusoidal inputs. 2.3 Dynamical accuracy of MIMO systems under slowly changing deterministic signals. 2.4 Statistical accuracy of linear MIMO systems. 2.5 Design of linear MIMO systems. Part II Nonlinear multivariable control systems. 3 Study of one-frequency self-oscillation in nonlinear harmonically linearized MIMO systems. 3.1 Introduction. 3.2 Mathematical foundations of the harmonic linearization method for one-frequency periodical processes in nonlinear MIMO systems. 3.3 One-frequency limit cycles in general MIMO systems. 3.4 Limit cycles in uniform MIMO systems. 3.5 Limit cycles in circulant and anticirculant MIMO systems. 4 Forced oscillation and generalized frequency response characteristics of nonlinear MIMO systems. 4.1 Introduction. 4.2 Nonlinear general MIMO systems. 4.3 Nonlinear uniform MIMO systems. 4.4 Forced oscillations and frequency response characteristics along the canonical basis axes of nonlinear circulant and anticirculant systems. 4.5 Design of nonlinear MIMO systems. 5 Absolute stability of nonlinear MIMO systems. 5.1 Introduction. 5.2 Absolute stability of general and uniform MIMO systems. 5.3 Absolute stability of normal MIMO systems. 5.4 Off-axis circle and parabolic criteria of the absolute stability of mimo systems. 5.5 Multidimensional circle criteria of absolute stability. 5.6 Multidimensional circle criteria of the absolute stability of forced motions. Bibliography. Index.
Pulmonalarterielle Hypertonie und kardiopulmonale Komorbidität

Zusammenfassung In den neuen Leitlinien für pulmonalarterielle Hypertonie (PAH, Gruppe 1) wird erstmals empfohlen, vor Therapiebeginn zwischen PAH-Patienten mit bzw. ohne kardiopulmonale Komorbiditäten zu unterscheiden. Hintergrund hierfür ist, dass einerseits in den zulassungsrelevanten Therapiestudien Patienten mit Komorbiditäten unterrepräsentiert bzw. ausgeschlossen waren, andererseits diese Gruppe aber bei Weitem den größten Anteil der PAH-Patienten in der klinischen Praxis stellen. Während Patienten mit Komorbiditäten von PAH-Medikamenten wie Phosphodiesterase-5-Inhibitoren zumeist als Monotherapie profitieren, ist eine Therapie der Patienten mit einer pulmonalen Hypertonie (PH) bei Linksherz- (Gruppe 2) oder Lungenerkrankung (Gruppe 3) mittels PAH-Medikamente nicht indiziert und kann z. T. sogar zu einer erhöhten Letalität führen. In diesem Artikel wird beschrieben, wie man PAH-Patienten mit Komorbiditäten von PH-Patienten der Gruppe 2 und 3 differenzieren kann. Die Unterscheidung und Stellung der Therapieindikation ist dabei oft nicht einfach und sollte in einem PH-Zentrum vorgenommen werden.
A revision of the solar abundance of dysprosium

The solar abundance of dysprosium is reevaluated from a new analysis of solar Dy II lines for which new accurate gf-values have recently been measured by Kusz (1992). The new result, A Dy = 1.14 ± 0.08, is in pretty good agreement with the meteoritic value
Influences of the Amorphous Phase on Local Structures and Properties of Ferroelectric Thin Films

The electrical properties of ferroelectric thin films are sensitive to structural disorders. However, the harmful structural defects are often difficult to be characterized by conventional characterization techniques. Here, we demonstrate that the local structures of lead zirconate titanate (PZT) ferroelectric thin films with different amorphous phase contents can be determined using x-ray absorption fine structure (XAFS) spectroscopy of synchrotron radiation. The results showed that XAFS spectroscopy is a powerful technique to quantify the amorphous phase content in ferroelectric thin films. Influences of the amorphous phase on local structures and properties of ferroelectric thin films were further discussed.
Incipient ferroelectricity and microwave dielectric resonance properties of CaCu2.85Mn0.15Ti4O12 ceramics

Mn-doped CaCu3Ti4O12 ceramics with nominal composition CaCu2.85Mn0. 15Ti4O12 (CCMTO) have been prepared and their radio- and micro-wave dielectric properties established. At 300 K, dense CCMTO ceramics have appreciable grain resistivity, ∼20MΩcm, and exhibit microwave dielectric resonance with er∼93, Qf∼3950GHz (at 3.95GHz) and temperature coefficient of resonant frequency ∼+657ppm∕K. er decreases smoothly from ∼150 to 90 in the range of 10–300K, obeys the Curie-Weiss law in the range of ∼60–180K, and is consistent with incipient ferroelectricity. The source of the incipient ferroelectricity and potential applications of CCMTO ceramics are discussed.
The interstellar methanol masers and their environments

To promote the understanding of massive star formation processes, we have studied the 6.6 GHz methanol (CH3OH) masers and their environments—the dense cores and the outer regions of the molecular cloud. The physics of the CH3OH maser or the thermal emission formation region is studied by fitting the observational data of the 6.6 GHz 51–60A+ and the 107 GHz 31–40A+CH3OH maser emission, using the radiative transfer calculations. The type II characteristics of the 6.6 GHz CH3OH maser are confirmed by the calculation results. A greater intensity of the radiation field leads to an increase in the peak intensity of the maser; however, high densities tend to turn off the maser. The calculation results show that to be a maser the 6.6 GHz CH3OH emission needs a radiation field of 150–300 K and a density not higher than 107cm−3, while the 107 GHz emission requires a radiation field of 210–300 K and a density not higher than 3×106 cm−3. The 6.6 GHz line is maser towards all six studied sources, while the 107 GHz line is maser towards Cep A only. Moreover, the former’s intensity is much stronger than the latter. The radiative transfer calculations also indicate that the 6.6 GHz maser emission is so strong that the requirements of its formation (e.g. the radiation field, the density and the kinetic parameters) can only be satisfied at a certain stage of the processes of the massive star formation. Therefore it is often used as one of the most prominent tracers for the massive star formation regions. The calculation results of the simutaneous observations of (1,1) through (4,4) inversion lines of the ammonia (NH3) indicate that both the temperature and the density in the 6.6 GHz CH3OH maser formation regions are higher than that of the NH3 line formation regions. Furthermore, the common fact of |Visr(CO)| > |Visr(NH3)|>|Visr(CH3OH 6.6GHz maser)| in all six sources implies the ongoing developing trends of those gas flows driven by the masers.
Trapped particles in toroidal magnetic systems

The review is devoted to the discussion of the role of trapped particles for equilibrium, diffusion and stability of plamas in toroidal magnetic devices. The motion of single particles in a toroidal magnetic field, the neoclassical transport processes due to the trapping of particles and trapped-particle instabilities in toroidal geometry are discussed. The correspondence between the neoclassical theory of diffusion, the turbulent transport processes due to the instabilities and the existing experimental Tokamak data is discussed.
The stabilisation of quantum computations

A quantum computer is a device capable of performing computational tasks that depend on characteristically quantum mechanical effects, in particular coherent quantum superposition. Such devices can efficiently perform classes of computation (e.g. factorisation) which are believed to be intractable on any classical computer. This makes it highly desirable to construct such devices. In this paper, we address the last remaining theoretical obstacle to such a construction, namely the problem of stability or error correction. This problem is more substantial in quantum computation than in classical computation because of the delicate nature of the interference phenomena on which quantum computation depends. We present a new, purely quantum mechanical method of error correction, which has no classical analogue, but can serve to stabilise coherent quantum computations. Like the classical methods, it utilises redundancy, but it does not depend on measuring intermediate results of the computation. <<ETX>>
Frequency-sum beamforming in an inhomogeneous environment

The arrival directions of ray paths between a sound source and a receiving array can be determined by beamforming the array-recorded signals. And, when the array and the signal are well matched, directional resolution increases with increasing signal frequency. However, when the environment between the source and the receivers is inhomogeneous, the recorded signal may be distorted and beamforming results may be increasingly degraded with increasing signal frequency. However, this sensitivity to inhomogeneities may be altered through use of an unconventional beamforming technique that manufactures higher frequency information by summing frequencies from lower-frequency signal components via a quadratic (or higher) product of complex signal amplitudes. This presentation will describe frequency-sum beamforming, and then illustrate it with simulation results and near-field acoustic experiments made with and without a thin plastic barrier between the source and the receiving array. The experiments were conduct.
A Shear-Based Parameterization of Turbulent Mixing in the Stable Atmospheric Boundary Layer

AbstractIn this study, shear-based parameterizations of turbulent mixing in the stable atmospheric boundary layer (SABL) are proposed. A relevant length-scale estimate for the mixing length of the turbulent momentum field is constructed from the turbulent kinetic energy and the mean shear rate S as . Using observational data from two field campaigns—the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment and the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99)— is shown to have a strong correlation with . The relationship between and corresponds to the ratio of the magnitude of the tangential components of the turbulent momentum flux tensor to , known as stress intensity ratio, . The field data clearly show that is linked to stability. The stress intensity ratio also depends on the flow energetics that can be assessed using a shear-production Reynolds number, , where P is shear production of turbulent kinetic energy and is the kinematic viscosity. This analysis shows that high mixing r.
Postoperatives Komplikationsmanagement nach Wirbelsäuleneingriffen: das postoperative Delir

Zusammenfassung Das postoperative Delir nach wirbelsäulenchirurgischen Eingriffen stellt eine häufige und schwerwiegende Komplikation dar. Die genaue Kenntnis von Risikofaktoren - wie z.B. ein vorangegangenes Delir, kognitive Einschränkungen, Einnahme delirogener Medikamente und Alkoholismus – hilft, Risikopatienten präoperativ zu identifizieren. Präventionsstrategien schließen nehmen der Prähabilitation (in erster Linie Verbesserung des Ernährungszustandes), das Ab- bzw. Umsetzen delirogener Medikamente, die strenge Indikationsstellung zu größeren operativen Eingriffen und das perioperative Blutungsmanagement ein. Standardisierte Tests erleichtern die postoperative Detektion eines Delirs. Bei der Behandlung steht die nicht-medikamentöse Therapie im Vordergrund. Sie schließt insbesondere die Kontinuierliche (Re)-Orientierung, Reizabschirmung, Homöostase, Schlafhygiene, rasche Mobilisierung und adäquate Therapie von Schmerzen und Infekten ein. Ist eine medikamentöse Therapie zusätzlich notwendig, empfiehlt sich Melperon oder Pipamperon für das hyperaktive Delir und Haloperidol bei starken Halluzinationen.
Recursive identification and adaptive prediction in linear stochastic systems

By making use of extended stochastic Lyapunov functions and martingale limit theorems, established herein are certain basic properties of adaptive d-step ahead predictors associated with the extended least squares, stochastic gradient (without interlacing), and monitored recursive maximum likelihood algorithms for recursive identification of an ARMAX system. Both the direct (or implicit) and indirect (or explicit) approaches to adaptive prediction are considered within a unified framework involving stochastic regression models. Applications to adaptive control of ARMAX systems are also discussed.