ShantanuT01/DACTYL-Pretraining huggingface dataset:
Breast cancer is becoming pervasive with each passing day. Hence, its early detection is a big step in saving the life of any patient. Mammography is a common tool in breast cancer diagnosis. The most important step here is classification of mammogram patches as normal-abnormal and benign-malignant.   Texture of a breast in a mammogram patch plays a significant role in these classifications. We propose a variation of Histogram of Gradients (HOG) and Gabor filter combination called Histogram of Oriented Texture (HOT) that exploits this fact. We also revisit the Pass Band - Discrete Cosine Transform (PB-DCT) descriptor that captures texture information well. All features of a mammogram patch may not be useful. Hence, we apply a feature selection technique called Discrimination Potentiality (DP). Our resulting descriptors, DP-HOT and DP-PB-DCT, are compared with the standard descriptors.   Density of a mammogram patch is important for classification, and has not been studied exhaustively. The Image Retrieval in Medical Application (IRMA) database from RWTH Aachen, Germany is a standard database that provides mammogram patches, and most researchers have tested their frameworks only on a subset of patches from this database. We apply our two new descriptors on all images of the IRMA database for density wise classification, and compare with the standard descriptors. We achieve higher accuracy than all of the existing standard descriptors (more than 92%).
Relative pose estimation is a fundamental problem in computer vision and it has been studied for conventional global shutter cameras for decades. However, recently, a rolling shutter camera has been widely used due to its low cost imaging capability and, since the rolling shutter camera captures the image line-by-line, the relative pose estimation of a rolling shutter camera is more difficult than that of a global shutter camera. In this paper, we propose to exploit inertial measurements (gravity and angular velocity) for the rolling shutter relative pose estimation problem. The inertial measurements provide information about the partial relative rotation between two views (cameras) and the instantaneous motion that causes the rolling shutter distortion. Based on this information, we simplify the rolling shutter relative pose estimation problem and propose effective methods to solve it. Unlike the previous methods, which require 44 (linear) or 17 (nonlinear) points with the uniform rolling shutter camera model, the proposed methods require at most 9 or 11 points to estimate the relative pose between the rolling shutter cameras. Experimental results on synthetic data and the public PennCOSYVIO dataset show that the proposed methods outperform the existing methods.
A perfect Euler cuboid is a rectangular parallelepiped with integer edges and integer face diagonals whose space diagonal is also integer. Such cuboids are not yet discovered and their non-existence is also not proved. Perfect Euler cuboids are described by a system of four Diophantine equation possessing a natural $S_3$ symmetry. Recently these equations were factorized with respect to this $S_3$ symmetry and the factor equations were derived. In the present paper the factor equations are transformed to $E$-form and then reduced to a single biquadratic equation.
We study phase transitions and the behavior of kaons in hot and dense matter, giving special attention to the role of strange quarks. At T=0, it is found that the fraction of the strange valence quarks affects the energy per particle of the system, without changing the nature of the phase transition, and, on the other side, it has meaningful effects on the behavior of kaons and antikaons masses. The phase behavior of kaons in the $T-\rho$ plane is analyzed in connection with the chiral phase transition.
In present paper, we prove the existence of solutions $(\lambda, u)\in \R\times H^1(\R^N)$ to the following Schr\"odinger equation $$ \begin{cases} -\Delta u(x)+V(x)u(x)+\lambda u(x)=g(u(x))\quad &\hbox{in}~\R^N\\ 0\leq u(x)\in H^1(\R^N), N\geq 3 \end{cases} $$ satisfying the normalization constraint $\displaystyle \int_{\R^N}u^2 dx=a$. We treat the so-called mass super-critical case here. Under an explicit smallness assumption on $V$ and some Ambrosetti-Rabinowitz type conditions on $g$, we can prove the existence of ground state normalized solutions for prescribed mass $a>0$. Furthermore, we emphasize that the mountain pass characterization of a minimizing solution of the problem $$\inf\left\{\int \left[\frac{1}{2}|\nabla u|^2+\frac{1}{2}V(x)u^2-G(u)\right]dx : \|u\|_{L^2(\R^N)}^{2}=a, P[u]=0\right\},$$ where $G(s)=\int_0^s g(\tau)d\tau$ and $$P[u]=\int\left[|\nabla u|^2-\frac{1}{2}\langle \nabla V(x), x\rangle u^2 -N\left(\frac{1}{2}g(u)u-G(u)\right)\right]dx.$$
For a nonnegative integer $n$, and a prime $\wp$ in $\mathbb{F}_q[T]$, we prove a result that provides a method for computing the number of integers $m$ with $0 \le m \le n$ for which the Carlitz binomial coefficients $\binom{n}{m}_C$ fall into each of the residue classes modulo $\wp$. Our main result can be viewed as a function field analogue of the Garfield-Wilf theorem.
A classical result states that the parity balance of the number of excedances of all permutations (derangements, respectively) of length $n$ is the Euler number. In 2010, Josuat-Verg\`{e}s gives a $q$-analogue with $q$ representing the number of crossings. We extend this result to the permutations (derangements, respectively) of type B and D. It turns out that the signed countings are related to the derivative polynomials of $\tan$ and $\sec$.   Springer numbers defined by Springer can be regarded as an analogue of Euler numbers defined on every Coxeter group. In 1992 Arnol'd showed that the Springer numbers of classical types A, B, D count various combinatorial objects, called snakes. In 1999 Hoffman found that derivative polynomials of $\sec x$ and $\tan x$ and their subtraction evaluated at certain values count exactly the number of snakes of certain types. Then Josuat-Verg\`{e}s studied the $(t,q)$-analogs of derivative polynomials $Q_n(t,q)$, $R_n(t,q)$ and showed that as setting $q=1$ the polynomials are enumerators of snakes with respect to the number of sign-changing. Our second result is to find combinatorial interpretations of $Q_n(t,q)$ and $R_n(t,q)$ as enumerators of the snakes, although the outcome is somewhat messy.
We investigate the degree of entanglement quantified by the concurrence of photon pairs that are simultaneously emitted in the biexciton-exciton cascade from a quantum dot in a cavity. Four dot-cavity configurations are compared that differ with respect to the detuning between the cavity modes and the quantum dot transitions, corresponding to different relative weights of direct two-photon and sequential single-photon processes. The dependence of the entanglement on the exciton fine-structure splitting $\delta$ is found to be significantly different for each of the four configurations. For a finite splitting and low temperatures, the highest entanglement is found when the cavity modes are in resonance with the two-photon transition between the biexciton and the ground state and, in addition, the biexciton has a finite binding energy of a few meV. However, this widely used configuration is rather strongly affected by phonons such that other dot-cavity configurations, that are commonly regarded as less suited for obtaining high degrees of entanglement, become more favorable already at temperatures on the order of 10 K and above. If the cavity modes are kept in resonance with one of the exciton-to-ground-state transitions and the biexciton binding energy is finite, the entanglement drastically drops for positive $\delta$ with rising temperatures when $T$ is below $\simeq$ 4 K, but is virtually independent of the temperature for higher $T$.
Considering the complex n-dimension Calabi-Yau homogeneous hyper-surfaces ${\cal H}_{n}$ and using algebraic geometry methods, we develop the crossed product algebra method, introduced by Berenstein et Leigh in hep-th/0105229, and build the non commutative (NC) geometries for orbifolds ${\cal O}={\cal H}_{n}/{\bf Z}_{n+2}^{n}$ with a discrete torsion matrix $t_{ab}=exp[{\frac{i2\pi}{n+2}}{(\eta_{ab}-\eta_{ba})}]$, $\eta_{ab} \in SL(n,{\bf Z})$. We show that the NC manifolds ${\cal O}^{(nc)}$ are given by the algebra of functions on the real $(2n+4)$ Fuzzy torus ${\cal T}^{2(n+2)}_{\beta_{ij}}$ with deformation parameters $\beta_{ij}=exp{\frac{i2\pi}{n+2}}{[(\eta^{-1}_{ab}-\eta^{-1}_{ba})} q_{i}^{a} q_{j}^{b}]$, $q_{i}^{a}$'s being Calabi-Yau charges of ${\bf Z}_{n+2}^{n}$. We develop graph rules to represent ${\cal O}^{(nc)}$ by quiver diagrams which become completely reducible at singularities. Generic points in these NC geometries are be represented by polygons with $(n+2)$ vertices linked by $(n+2)$ edges while singular ones are given by $(n+2)$ non connected loops. We study the various singular spaces of quintic orbifolds and analyze the varieties of fractional $D$ branes at singularities as well as the spectrum of massless fields. Explicit solutions for the NC quintic ${\cal Q}^{(nc)}$ are derived with details and general results for complex $n$ dimension orbifolds with discrete torsion are presented.
As nanoelectronics approaches the nanometer scale, a massive effort is underway to identify the next scalable logic technology beyond Complementary Metal Oxide Semiconductor (CMOS) computing. Such computing technology needs to improve switching energy & delay at reduced dimensions, allow improved interconnects and provide a complete logic/memory family. However, a viable beyond-CMOS logic technology has remained elusive. Here, we propose a scalable spintronic logic device which operates via spin-orbit transduction combined with magneto-electric switching. The proposed Magneto-Electric Spin Orbit (MESO) logic enables a new paradigm to continue scaling of logic performance to near thermodynamic limits for GHz logic (100 kT switching energy at 100 ps delay). The proposed MESO devices scale strongly and favorably with critical dimensions of the device, showing a cubic dependence of switching energy on size, (E_m proportional to W^3), and square dependence on voltage (E_m proportional to V^2). The excellent scaling is obtained thanks to the properties of the spin orbit effects (e.g. Inverse Spin Hall Effect (ISHE) and Inverse Rashba-Edelstein Effect (IREE)) and the dependence of capacitance on size. The operating voltages for these devices are predicted to be < 100 mV allowing a significant jump ahead of historic trends of scaling voltage with size and corresponding reduction of energy. Interconnect resistance is a critical obstacle for scaling beyond 10 nm dimensions. We project a less detrimental impact of interconnect resistance and show that MESO logic is amenable for highly resistive interconnects (100 uOhm.cm-1 mOhm.cm) which opens a possibility to use nano-metallic (width < bulk electron mean free path) or doped semiconducting wires (width<5 nm). A scalable, CMOS compatible, non-volatile logic family proposed here may enable the next multi-generational scaling of computing devices.
Light emission spectrum from a scanning tunnelling microscope (LESTM) is investigated as a function of relative humidity and shown to be a novel and sensitive means for probing the growth and properties of a water meniscus in the nm-scale. An empirical model of the light emission process is formulated and applied successfully to replicate the decay in light intensity and spectral changes observed with increasing relative humidity. The modelling indicates a progressive water filling of the tip-sample junction with increasing humidity or, more pertinently, of the volume of the localized surface plasmons responsible for light emission; it also accounts for the effect of asymmetry in structuring of the water molecules with respect to polarity of the applied bias. This is juxtaposed with the case of a non-polar liquid in the tip-sample nano cavity where no polarity dependence of the light emission is observed. In contrast to the discrete detection of the presence/absence of water bridge in other scanning probe experiments by measurement of the feedback parameter for instrument control LESTM offers a means of continuously monitoring the development of the water bridge with sub-nm sensitivity. The results are relevant to applications such as dip-pen nanolithography and electrochemical scanning probe microscopy.
The neutron star (NS) low-mass X-ray binary (LMXB) the Rapid Burster (RB; MXB 1730-335) uniquely shows both Type-I and Type-II X-ray bursts. The origin of the latter is ill-understood but has been linked to magnetospheric gating of the accretion flow. We present a spectral analysis of simultaneous Swift, NuSTAR and XMM-Newton observations of the RB during its 2015 outburst. Although a broad Fe-K line has been observed before, the high quality of our observations allows us to model this line using relativistic reflection models for the first time. We find that the disk is strongly truncated at $41.8^{+6.7}_{-5.3}$ gravitational radii ($\sim 87$ km), which supports magnetospheric Type-II burst models and strongly disfavors models involving instabilities at the innermost stable circular orbit. Assuming that the RB magnetic field indeed truncates the disk, we find $B = (6.2 \pm 1.5) \times 10^8$ G, larger than typically inferred for NS LMXBs. In addition, we find a low inclination ($i = 29\pm2^{\rm o}$). Finally, we comment on the origin of the Comptonized and thermal components in the RB spectrum.
We present a systematic semiclassical model for the simulation of the dynamics of a single two-level atom strongly coupled to a driven high-finesse optical cavity. From the Fokker-Planck equation of the combined atom-field Wigner function we derive stochastic differential equations for the atomic motion and the cavity field. The corresponding noise sources exhibit strong correlations between the atomic momentum fluctuations and the noise in the phase quadrature of the cavity field. The model provides an effective tool to investigate localisation effects as well as cooling and trapping times. In addition, we can continuously study the transition from a few photon quantum field to the classical limit of a large coherent field amplitude.
Disorder is generically anticipated to suppress long range charge density wave (CDW) order. We report transport, thermodynamic, and scattering experiments on Pd$_x$ErTe$_3$, a model CDW system with disorder induced by intercalation. The pristine parent compound ($x=0$) shows two separate, mutually perpendicular, incommensurate unidirectional CDW phases setting in at 270 K and 165 K. Here we track the suppression of signatures corresponding to these two parent transitions as the Pd concentration increases. At the largest values of $x$, we observe complete suppression of long range CDW order in favor of superconductivity. We also report evidence from electron and x-ray diffraction which suggests a tendency toward short-range ordering along both wavevectors which persists even well above the crossover temperature. Pd$_x$ErTe$_3$ provides a promising model system for the study of the interrelation of charge order and superconductivity in the presence of quenched disorder.
Let $X$ be a super-Brownian motion (SBM) defined on a domain $E\subset R^n$ and $(X_D)$ be its exit measures indexed by sub-domains of $E$. The relationship between the equation $1/2 \Delta u=2 u^2$ and Super-Brownian motion (SBM) is analogous to the relationship between Brownian motion and the Laplace's equation, and substantial progress has been made on the study of the solutions of this semi-linear p.d.e. exploring this analogy. An area that remains to be explored is Martin boundary theory. Martin boundary in the semi-linear case is defined as the convex set of extreme $X$-harmonic functions which are functions on the space of finite measures supported in a domain $E$ of $R^d$ and characterized by a mean value property with respect to the Super-Brownian law. So far no probabilistic construction of Martin boundary is known.   In this paper, we consider a bounded smooth domain $D$, and we investigate exit densities of SBM, a certain family of $X$ harmonic functions, $H^{\nu}$, indexed by finite measures $\nu$ on $\partial{D}$, These densities were first introduced by E.B. Dynkin and also identified by T.Salisbury and D. Sezer as the extended X-harmonic functions corresponding to conditioning SBM on its exit measure $X_D$ being equal to $\nu$. $H^{\nu}(\mu)$ can be thought as the analogue of the Poisson kernel for Brownian motion. It is well known that Poisson kernel for a smooth domain $D$ is equivalent to the so called Martin kernel, the class of extreme harmonic functions for $D$. We show that a similar result is true for Super-Brownian motion as well, that is $H^{\nu}$ is extreme for almost all $\nu$ with respect to a certain measure.
We consider the high gain spontaneous parametric down-conversion in a non collinear geometry as a paradigmatic scenario to investigate the quantum-to-classical transition by increasing the pump power, that is, the average number of generated photons. The possibility of observing quantum correlations in such macroscopic quantum system through dichotomic measurement will be analyzed by addressing two different measurement schemes, based on different dichotomization processes. More specifically, we will investigate the persistence of non-locality in an increasing size n/2-spin singlet state by studying the change in the correlations form as $n$ increases, both in the ideal case and in presence of losses. We observe a fast decrease in the amount of Bell's inequality violation for increasing system size. This theoretical analysis is supported by the experimental observation of macro-macro correlations with an average number of photons of about 10^3. Our results enlighten the practical extreme difficulty of observing non-locality by performing such a dichotomic fuzzy measurement.
We discuss what can be learned about the shape of the pion distribution amplitude from the form factor for gamma* gamma(*) to pi transitions.
Gamma rays reveal extreme, nonthermal conditions in the Universe. The Fermi Gamma-ray Space Telescope has been exploring the gamma-ray sky for more than four years, enabling a search for powerful transients like gamma-ray bursts, solar flares, and flaring active galactic nuclei, as well as long-term studies including pulsars, binary systems, supernova remnants, and searches for predicted sources of gamma rays such as clusters of galaxies. Some results include a stringent limit on Lorentz invariance violation derived from a gamma-ray burst, unexpected gamma-ray variability from the Crab Nebula, a huge gamma-ray structure in the direction of the center of our Galaxy, and strong constraints on some Weakly Interacting Massive Particle (WIMP) models for dark matter.
We investigate the ground-state phase diagram of the half-filled one-dimensional Hubbard model with next-nearest-neighbor hopping using the Density-Matrix Renormalization Group technique as well as an unrestricted Hartree-Fock approximation. We find commensurate and incommensurate disordered magnetic insulating phases and a spin-gapped metallic phase in addition to the one-dimensional Heisenberg phase. At large on-site Coulomb repulsion $U$, we make contact with the phase diagram of the frustrated Heisenberg chain, which has spin-gapped phases for sufficiently large frustration. For weak $U$, sufficiently large next-nearest-neighbor hopping $t_2$ leads to a band structure with four Fermi points rather than two, producing a spin-gapped metallic phase. As $U$ is increased in this regime, the system undergoes a Mott-Hubbard transition to a frustrated antiferromagnetic insulator.
In this paper, we define the constant $D(\varphi, p)$, an analogue for the Davenport constant, for sequences on the finite field $\mathbb{F}_p$, defined via quadratic symmetric polynomials. Next, we state a series of results presenting either the exact value of $D(\varphi, p)$, or lower and upper bounds for this constant.
We prove gradient estimates for solutions of the oblique derivative problem for a large class of elliptic and parabolic quasilinear PDEs. In particular, we expand on previous work of the author using a maximum principle argument. In addition, we prove estimates for the parabolic problem of evolution via mean curvature with nonzero Neumann data, which seem to be new.
An oscillatory pattern in the smoothed quantum spectrum, which is unique for single-particle motions in a reflection-asymmetric superdeformed oscillator potential, is investigated by means of the semiclassical theory of shell structure. Clear correspondence between the oscillating components of the smoothed level density and the classical periodic orbits is found. It is shown that an interference effect between two families of the short periodic orbits, called supershell effect, develops with increasing reflection-asymmetric deformations. Possible origins of this enhancement phenomena as well as quantum signatures of period-multipling bifurcations are discussed in connection with stabilities of the classical periodic orbits.
We present a short proof of Klartag's central limit theorem for convex bodies, using only the most classical facts about log-concave functions. An appendix is included where we give the proof that thin shell implies CLT. The paper is accessible to anyone.
Recently, Gross claims that Boltzmann entropy $S=k\ln W$ is valid for any system at equilibrium, so that Tsallis entropy is useless in this case. I comment on some arguments forwarded to reach this conclusion and argue that the additive energy formalism of nonextensive statistics is not appropriate for the fundamental study of the theory for nonadditive systems.
In this short note we observe that recent results of Abert and Hubai and of Csikvari and Frenkel about Benjamini--Schramm continuity of the holomorphic moments of the roots of the chromatic polynomial extend to the theory of dense graph sequences. We offer a number of problems and conjectures motivated by this observation.
The effect of correlations between the slope and the curvature of the symmetry energy on ground state nuclear observables is studied within the extended Thomas-Fermi approximation. We consider different isovector probes of the symmetry energy, with a special focus on the skin of $^{208}{\rm Pb}$. We use a recently proposed meta-modelling technique to generate a large number of equation of state models, where the empirical parameters are independently varied. The results are compared to a set of calculations using 17 different Skyrme interactions. We show that the curvature parameter plays a non-negligible role on the neutron skin, while the effect is reduced in Skyrme functionals because of the correlation with the slope parameter.
Recently, Chappelon and Alfons\'{\i}n defined the square Frobenius number of coprime numbers $m$ and $n$ to be the largest perfect square that cannot be expressed in the form $mx+ny$ for nonnegative integers $x$ and $y$. When $m$ and $n$ differ by $1$ or $2$, they found simple expressions if neither $m$ nor $n$ is a perfect square. If either $m$ or $n$ is a perfect square, they formulated some interesting conjectures which have an unexpected close connection with a known recursive sequence, related to the denominators of Farey fraction approximations to $\sqrt{2}$. In this note, we prove these conjectures. Our methods involve solving Pell's equations $x^2-2y^2=1$ and $x^2-2y^2=-1$. Finally, to complete our proofs of these conjectures, we eliminate several cases using a bunch of results related to solutions of simultaneous Pell's equations.
We show how entangled valence-bond singlet pairs are disentangled partially and totally by the Kennedy-Tasaki transformation which reveals the hidden $Z_2\times Z_2$ symmetry in valence-bond-solid chains as a higher-spin generalization of the previous studies toward the intermediate-$D$ state. The totally disentangled states correspond to four Ising-like states with $Z_2$ variables on the boundary. We present a simple expression of results by using the spin decomposition and the boundary matrix.