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M. A. Rodriguez

Publications and source records attributed to M. A. Rodriguez.

At least 19 recordsLinked to original sources
arXiv2022

Multi-Label Retinal Disease Classification using Transformers

Early detection of retinal diseases is one of the most important means of preventing partial or permanent blindness in patients. In this research, a novel multi-label classification system is proposed for the detection of multiple retinal diseases, using fundus images collected from a variety of sources. First, a new multi-label retinal disease dataset, the MuReD dataset, is constructed, using a number of publicly available datasets for fundus disease classification. Next, a sequence of post-processing steps is applied to ensure the quality of the image data and the range of diseases, present in the dataset. For the first time in fundus multi-label disease classification, a transformer-based model optimized through extensive experimentation is used for image analysis and decision making. Numerous experiments are performed to optimize the configuration of the proposed system. It is shown that the approach performs better than state-of-the-art works on the same task by 7.9% and 8.1% in terms of AUC score for disease detection and disease classification, respectively. The obtained results further support the potential applications of transformer-based architectures in the medical imaging field.

cs.CV↗
arXiv2022

Evidence of decoupling of surface and bulk states in Dirac semimetal $Cd_{3}As_{2}$

Dirac semimetals have attracted a great deal of current interest due to their potential applications in topological quantum computing, low-energy electronic applications, and single photon detection in the microwave frequency range. Herein are results from analyzing the low magnetic (B) field weak-antilocalization behaviors in a Dirac semimetal $Cd_{3}As_{2}$ thin flake device. At high temperatures, the phase coherence length $l_ϕ$ first increases with decreasing temperature (T) and follows a power law dependence of $l_ϕ\propto$ T$^{-0.4}$. Below ~ 3K, $l_ϕ$ tends to saturate to a value of ~ 180 nm. Another fitting parameter $α$, which is associated with independence transport channels, displays a logarithmic temperature dependence for T > 3K, but also tends to saturate below ~ 3K. The saturation value, ~ 1.45, is very close to 1.5, indicating three independent electron transport channels, which we interpret as due to decoupling of both the top and bottom surfaces as well as the bulk. This result, to our knowledge, provides first evidence that the surfaces and bulk states can become decoupled in electronic transport in Dirac semimetal $Cd_{3}As_{2}$.

cond-mat.mes-hall↗
arXiv2020

Zero Bias Conductance Peak in Dirac Semimetal-Superconductor Devices

Majorana zero modes (MZMs), fundamental building blocks for realizing topological quantum computers, can appear at the interface between a superconductor and a topological material. One of the experimental signatures that has been widely pursued to confirm the existence of MZMs is the observation of a large, quantized zero-bias conductance peak (ZBCP) in the differential conductance measurements. In this Letter, we report observation of such a large ZBCP in junction structures of normal metal (titanium/gold Ti/Au) + Dirac semimetal (cadmium arsenide Cd3As2) + conventional superconductor (aluminum Al), with a value close to four times that of the normal state conductance. Our detailed analyses suggest that this large ZBCP is most likely not caused by MZMs. We attribute the ZBCP, instead, to the existence of a supercurrent between two far-separated superconducting Al electrodes, which shows up as a zero-bias peak because of the circuitry and thermal fluctuations of the supercurrent phase, a mechanism conceived by Ivanchenko and Zil'berman more than 50 years ago [JETP 28, 1272 (1969)]. Our results thus call for extreme caution when assigning the origin of a large ZBCP to MZMs in a multiterminal semiconductor or topological insulator/semimetal setup. We thus provide criteria for identifying when the ZBCP is definitely not caused by an MZM. Furthermore, we present several remarkable experimental results of a supercurrent effect occurring over unusually long distances and clean perfect Andreev reflection features.

cond-mat.mes-hall↗
arXiv2015

Nilpotent integrability, reduction of dynamical systems and a third-order Calogero-Moser system

We present an algebraic formulation of the notion of integrability of dynamical systems, based on a nilpotency property of its flow: it can be explicitly described as a polynomial on its evolution parameter. Such a property is established in a purely geometric--algebraic language, in terms both of the algebra of all higher-order constants of the motion (named the nilpotent algebra of the dynamics), and of a maximal Abelian algebra of symmetries (called a Cartan subalgebra of the dynamics). It is shown that this notion of integrability amounts to the annihilator of the nilpotent algebra being contained in a Cartan subalgebra of the dynamics. Systems exhibiting this property will be said to be nilpotent integrable. Our notion of nilpotent integrability offers a new insight into the intrinsic dynamical properties of a system, which is independent of any auxiliary geometric structure defined on its phase space. At the same time, it extends in a natural way the classical concept of complete integrability for Hamiltonian systems. An algebraic reduction procedure valid for nilpotent integrable systems, generalizing the well-known reduction procedures for symplectic and/or Poisson systems on appropriate quotient spaces, is also discussed. In particular, it is shown that a large class of nilpotent integrable systems can be obtained by reduction of higher-order free systems. The case of the third-order free system is analyzed and a nontrivial set of third-order Calogero-Moser-like nilpotent integrable equations is obtained.

math-ph↗
arXiv2010

Inozemtsev's hyperbolic spin model and its related spin chain

In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm-Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane-Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos.

math-ph↗
arXiv2010

$λ$-symmetries for discrete equations

Following the usual definition of $λ$-symmetries of differential equations, we introduce the analogous concept for difference equations and apply it to some examples.

math-ph↗
arXiv2009

Symmetry reduction and superintegrable Hamiltonian systems

We construct complete sets of invariant quantities that are integrals of motion for two Hamiltonian systems obtained through a reduction procedure, thus proving that these systems are maximally superintegrable. We also discuss the reduction method used in this article and its possible generalization to other maximally superintegrable systems.

math-ph↗
arXiv2009

$1/f^α$ noise and integrable systems

An innovative test for detecting quantum chaos based on the analysis of the spectral fluctuations regarded as a time series has been recently proposed. According to this test, the fluctuations of a fully chaotic system should exhibit 1/f noise, whereas for an integrable system this noise should obey the 1/f^2 power law. In this letter, we show that there is a family of well-known integrable systems, namely spin chains of Haldane-Shastry type, whose spectral fluctuations decay instead as 1/f^4. We present a simple theoretical justification of this fact, and propose an alternative characterization of quantum chaos versus integrability formulated directly in terms of the power spectrum of the spacings of the unfolded spectrum.

nlin.CD↗
arXiv2008

An exactly solvable supersymmetric spin chain of BC_N type

We construct a new exactly solvable supersymmetric spin chain related to the BC_N extended root system, which includes as a particular case the BC_N version of the Polychronakos-Frahm spin chain. We also introduce a supersymmetric spin dynamical model of Calogero type which yields the new chain in the large coupling limit. This connection is exploited to derive two different closed-form expressions for the chain's partition function by means of Polychronakos's freezing trick. We establish a boson-fermion duality relation for the new chain's spectrum, which is in fact valid for a large class of (not necessarily integrable) spin chains of BC_N type. The exact expressions for the partition function are also used to study the chain's spectrum as a whole, showing that the level density is normally distributed even for a moderately large number of particles. We also determine a simple analytic approximation to the distribution of normalized spacings between consecutive levels which fits the numerical data with remarkable accuracy. Our results provide further evidence that spin chains of Haldane-Shastry type are exceptional integrable models, in the sense that their spacings distribution is not Poissonian, as posited by the Berry-Tabor conjecture for "generic'' quantum integrable systems.

hep-th↗
arXiv2008

The Berry-Tabor conjecture for spin chains of Haldane-Shastry type

According to a long-standing conjecture of Berry and Tabor, the distribution of the spacings between consecutive levels of a "generic'' integrable model should follow Poisson's law. In contrast, the spacings distribution of chaotic systems typically follows Wigner's law. An important exception to the Berry-Tabor conjecture is the integrable spin chain with long-range interactions introduced by Haldane and Shastry in 1988, whose spacings distribution is neither Poissonian nor of Wigner's type. In this letter we argue that the cumulative spacings distribution of this chain should follow the "square root of a logarithm'' law recently proposed by us as a characteristic feature of all spin chains of Haldane-Shastry type. We also show in detail that the latter law is valid for the rational counterpart of the Haldane-Shastry chain introduced by Polychronakos.

hep-th↗
arXiv2008

The Polychronakos-Frahm spin chain of BC_N type and Berry-Tabor's conjecture

We compute the partition function of the su(m) Polychronakos-Frahm spin chain of BC_N type by means of the freezing trick. We use this partition function to study several statistical properties of the spectrum, which turn out to be analogous to those of other spin chains of Haldane-Shastry type. In particular, we find that when the number of particles is sufficiently large the level density follows a Gaussian distribution with great accuracy. We also show that the distribution of (normalized) spacings between consecutive levels is of neither Poisson nor Wigner type, but is qualitatively similar to that of the original Haldane-Shastry spin chain. This suggests that spin chains of Haldane-Shastry type are exceptional integrable models, since they do not satisfy a well-known conjecture of Berry and Tabor according to which the spacings distribution of a generic integrable system should be Poissonian. We derive a simple analytic expression for the cumulative spacings distribution of the BC_N-type Polychronakos-Frahm chain using only a few essential properties of its spectrum, like the Gaussian character of the level density and the fact the energy levels are equally spaced. This expression is in excellent agreement with the numerical data and, moreover, there is strong evidence that it can also be applied to the Haldane-Shastry and the Polychronakos-Frahm spin chains.

cond-mat.stat-mech↗
arXiv2007

Exchange operator formalism for N-body spin models with near-neighbors interactions

We present a detailed analysis of the spin models with near-neighbors interactions constructed in our previous paper [Phys. Lett. B 605 (2005) 214] by a suitable generalization of the exchange operator formalism. We provide a complete description of a certain flag of finite-dimensional spaces of spin functions preserved by the Hamiltonian of each model. By explicitly diagonalizing the Hamiltonian in the latter spaces, we compute several infinite families of eigenfunctions of the above models in closed form in terms of generalized Laguerre and Jacobi polynomials.

nlin.SI↗
arXiv2007

A novel quasi-exactly solvable spin chain with nearest-neighbors interactions

In this paper we study a novel spin chain with nearest-neighbors interactions depending on the sites coordinates, which in some sense is intermediate between the Heisenberg chain and the spin chains of Haldane-Shastry type. We show that when the number of spins is sufficiently large both the density of sites and the strength of the interaction between consecutive spins follow the Gaussian law. We develop an extension of the standard freezing trick argument that enables us to exactly compute a certain number of eigenvalues and their corresponding eigenfunctions. The eigenvalues thus computed are all integers, and in fact our numerical studies evidence that these are the only integer eigenvalues of the chain under consideration. This fact suggests that this chain can be regarded as a finite-dimensional analog of the class of quasi-exactly solvable Schroedinger operators, which has been extensively studied in the last two decades. We have applied the method of moments to study some statistical properties of the chain's spectrum, showing in particular that the density of eigenvalues follows a Wigner-like law. Finally, we emphasize that, unlike the original freezing trick, the extension thereof developed in this paper can be applied to spin chains whose associated dynamical spin model is only quasi-exactly solvable.

hep-th↗
arXiv2006

Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials

We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial modification of the exchange operator formalism is used to obtain several infinite families of eigenfunctions of these models in closed form.

nlin.SI↗
arXiv2005

Anomalous Roughening of Viscous Fluid Fronts in Spontaneous Imbibition

We report experiments on spontaneous imbibition of a viscous fluid by a model porous medium in the absence of gravity. The average position of the interface satisfies Washburn's law. Scaling of the interface fluctuations provides a dynamic exponent z \simeq 3, indicative of global dynamics driven by capillary forces. The complete set of exponents clearly shows that interfaces are not self-affine, exhibiting distinct local and global scaling, both for time (b=0.64\pm 0.02, b* =0.33 \pm 0.03) and space (a=1.94 \pm 0.20, a_loc=0.94 \pm 0.10). These values are compatible with an intrinsic anomalous scaling scenario.

cond-mat.dis-nn↗
arXiv2004

Haldane-Shastry spin chains of BC_N type

We introduce four types of SU(2M+1) spin chains which can be regarded as the BC_N versions of the celebrated Haldane-Shastry chain. These chains depend on two free parameters and, unlike the original Haldane-Shastry chain, their sites need not be equally spaced. We prove that all four chains are solvable by deriving an exact expression for their partition function using Polychronakos's "freezing trick". From this expression we deduce several properties of the spectrum, and advance a number of conjectures that hold for a wide range of values of the spin M and the number of particles. In particular, we conjecture that the level density is Gaussian, and provide a heuristic derivation of general formulas for the mean and the standard deviation of the energy.

hep-th↗