arXiv subjects

Alfonso Martinez

Publications and source records attributed to Alfonso Martinez.

At least 19 recordsLinked to original sources

arXiv2026

The quantum multinomial distribution: a combinatorial formulation of multiphoton interference

This paper presents a quantum generalization of the multinomial distribution for the transition probabilities of $m$ identical photons in a $k$-port linear optical interferometer: two multinomial coefficients (one for the input configuration, one for the output) times the squared modulus of a coherent sum over routing matrices, weighted by the multivariate hypergeometric distribution; no Hilbert space formalism is needed to state or evaluate it. The classical multinomial is recovered when all photons enter through a single port, the coherent sum degenerating to a single term with no interference; the quantum family is not a generalization in the Askey sense but a parallel family that departs from classical statistics through the coherence of the amplitude summation. The $r$-th factorial moment carries a squared multinomial coefficient in place of the classical single one, the extra factor arising from the two copies of the amplitude expansion whose indices the Fock state forces to agree; for the beam splitter, the third cumulant is invariant under bosonic interference and the quantum departure first appears in the fourth cumulant as negative excess kurtosis; for multiport interferometers, however, three-body interference breaks this invariance and the departure enters already at the third cumulant. Cross-mode covariances involve the phases of the scattering matrix through coherence terms that strengthen output anti-correlations beyond the classical value; together with the squared-coefficient signature in the single-mode moments, these provide low-order statistical witnesses for boson sampling verification without requiring the full permanent computation.

quant-ph↗

arXiv2025

Instantaneous Core Loss -- Cycle-by-cycle Modeling of Power Magnetics in PWM DC-AC Converters

Nowadays, PWM excitation is one of the most common waveforms seen by magnetic components in power electronic converters. Core loss modelling approaches such as improved Generalized Steinmetz equation (iGSE) or the loss map based on composite waveform hypothesis (CWH) process the PWM excitation piecewisely, which is proven to be effective for DC DC converters. As the additional challenge in PWM DC AC converters, the fundamental-frequency sinewave component induces the "major loop loss" on top of the piecewise high-frequency segments, which however cannot be modelled on a switching cycle basis by any existing methods. To address this gap, this paper proposes a novel fundamental concept, instantaneous core loss, which is the time-domain core loss observed experimentally for the first time in history. Extending the reactive voltage cancellation concept, this work presents a method to measure the instantaneous core loss, which only contains real power loss, as a function of time. Based on measurements in evaluated soft magnetic components, it was discovered that the discharging stage exhibits higher core loss than the charging stage. A modelling approach is then proposed to break down the major loop core loss, typically an average value in the literature, into the time domain to enable cycle-by-cycle modelling of core losses in PWM converters. This work enhances the fundamental understanding of the core loss process by moving from the average model to the time-domain model.

eess.SY↗

arXiv2023

Information-Theoretic Foundations of Mismatched Decoding

Shannon's channel coding theorem characterizes the maximal rate of information that can be reliably transmitted over a communication channel when optimal encoding and decoding strategies are used. In many scenarios, however, practical considerations such as channel uncertainty and implementation constraints rule out the use of an optimal decoder. The mismatched decoding problem addresses such scenarios by considering the case that the decoder cannot be optimized, but is instead fixed as part of the problem statement. This problem is not only of direct interest in its own right, but also has close connections with other long-standing theoretical problems in information theory. In this monograph, we survey both classical literature and recent developments on the mismatched decoding problem, with an emphasis on achievable random-coding rates for memoryless channels. We present two widely-considered achievable rates known as the generalized mutual information (GMI) and the LM rate, and overview their derivations and properties. In addition, we survey several improved rates via multi-user coding techniques, as well as recent developments and challenges in establishing upper bounds on the mismatch capacity, and an analogous mismatched encoding problem in rate-distortion theory. Throughout the monograph, we highlight a variety of applications and connections with other prominent information theory problems.

cs.IT↗

arXiv2021

On the Angular Momentum and Spin of Generalized Electromagnetic Field for $r$-Vectors in $(k,n)$ Space-Time Dimensions

This paper studies the relativistic angular momentum for the generalized electromagnetic field, described by $r$-vectors in $(k,n)$ space-time dimensions, with exterior-algebraic methods. First, the angular-momentum tensor is derived from the invariance of the Lagrangian to space-time rotations (Lorentz transformations), avoiding the explicit need of the canonical tensor in Noether's theorem. The derivation proves the conservation law of angular momentum for generic values of $r$, $k$, and $n$. Second, an integral expression for the flux of the tensor across a $(k+n-1)$-dimensional surface of constant $\ell$-th space-time coordinate is provided in terms of the normal modes of the field; this analysis is a natural generalization of the standard analysis of electromagnetism, i. e. a three-dimensional space integral at constant time. Third, a brief discussion on the orbital angular momentum and the spin of the generalized electromagnetic field, including their expression in complex-valued circular polarizations, is provided for generic values of $r$, $k$, and $n$.

math-ph↗

arXiv2021

An Exterior Algebraic Derivation of the Euler-Lagrange Equations from the Principle of Stationary Action

In this paper, we review two related aspects of field theory: the modeling of the fields by means of exterior algebra and calculus, and the derivation of the field dynamics, i.e., the Euler-Lagrange equations, by means of the stationary action principle. In contrast to the usual tensorial derivation of these equations for field theories, that gives separate equations for the field components, two related coordinate-free forms of the Euler-Lagrange equations are derived. These alternative forms of the equations, reminiscent of the formulae of vector calculus, are expressed in terms of vector derivatives of the Lagrangian density. The first form is valid for a generic Lagrangian density that only depends on the first-order derivatives of the field. The second form, expressed in exterior algebra notation, is specific to the case when the Lagrangian density is a function of the exterior and interior derivatives of the multivector field. As an application, a Lagrangian density for generalized electromagnetic multivector fields of arbitrary grade is postulated and shown to have, by taking the vector derivative of the Lagrangian density, the generalized Maxwell equations as Euler--Lagrange equations.

math-ph↗

arXiv2021

Generalized Maxwell equations for exterior-algebra multivectors in $(k,n)$ space-time dimensions

This paper presents an exterior-algebra generalization of electromagnetic fields and source currents as multivectors of grades $r$ and $r-1$ respectively in a flat space-time with $n$ space and $k$ time dimensions. Formulas for the Maxwell equations and the Lorentz force for arbitrary values of $r$, $n$, and $k$ are postulated in terms of interior and exterior derivatives, in a form that closely resembles their vector-calculus analogues. These formulas lead to solutions in terms of potentials of grade $r-1$, and to conservation laws in terms of a stress-energy-momentum tensor of rank 2 for any values of $r$, $n$, and $k$, for which a simple explicit formula is given. As an application, an expression for the flux of the stress-energy-momentum tensor across an $(n+k-1)$-dimensional slice of space-time is given in terms of the Fourier transform of the potentials. The abstraction of Maxwell equations with exterior calculus combines the simplicity and intuitiveness of vector calculus, as the formulas admit explicit expressions, with the power of tensors and differential forms, as the formulas can be given for any values of $r$, $n$, and $k$.

math-ph↗

arXiv2021

An exterior-algebraic derivation of the symmetric stress-energy-momentum tensor in flat space-time

This paper characterizes the symmetric rank-2 stress-energy-momentum tensor associated with fields whose Lagrangian densities are expressed as the dot product of two multivector fields, e. g., scalar or gauge fields, in flat space-time. The tensor is derived by a direct application of exterior-algebraic methods to deal with the invariance of the action to infinitesimal space-time translations; this direct derivation avoids the use of the canonical tensor. Formulas for the tensor components and for the tensor itself are derived for generic values of the multivector grade $s$ and of the number of time and space dimensions, $k$ and $n$, respectively. A simple, coordinate-free, closed-form expression for the interior derivative (divergence) of the symmetric stress-energy-momentum tensor is also obtained: this expression provides a natural generalization of the Lorentz force that appears in the context of the electromagnetic theory. Applications of the formulas derived in this paper to the cases of generalized electromagnetism, Proca action, Yang-Mills fields and conformal invariance are briefly discussed.

physics.gen-ph↗

arXiv2020

An Introduction to Space-Time Exterior Calculus

The basic concepts of exterior calculus for space-time multivectors are presented: interior and exterior products, interior and exterior derivatives, oriented integrals over hypersurfaces, circulation and flux of multivector fields. Two Stokes theorems relating the exterior and interior derivatives with circulation and flux respectively are derived. As an application, it is shown how the exterior-calculus space-time formulation of the electromagnetic Maxwell equations and Lorentz force recovers the standard vector-calculus formulations, in both differential and integral forms.

math-ph↗

arXiv2019

Joint Source-Channel Coding for the Multiple-Access Channel with Correlated Sources

This paper studies the random-coding exponent of joint source-channel coding for the multiple-access channel with correlated sources. For each user, by defining a threshold, the messages of each source are partitioned into two classes. The achievable exponent for correlated sources with two message-dependent input distributions for each user is determined and shown to be larger than that achieved using only one input distribution for each user. A system of equations is presented to determine the optimal thresholds maximizing the achievable exponent. The obtained exponent is compared with the one derived for the MAC with independent sources.

cs.IT↗

arXiv2019

Augmenting Gastrointestinal Health: A Deep Learning Approach to Human Stool Recognition and Characterization in Macroscopic Images

Purpose - Functional bowel diseases, including irritable bowel syndrome, chronic constipation, and chronic diarrhea, are some of the most common diseases seen in clinical practice. Many patients describe a range of triggers for altered bowel consistency and symptoms. However, characterization of the relationship between symptom triggers using bowel diaries is hampered by poor compliance and lack of objective stool consistency measurements. We sought to develop a stool detection and tracking system using computer vision and deep convolutional neural networks (CNN) that could be used by patients, providers, and researchers in the assessment of chronic gastrointestinal (GI) disease.

cs.LG↗

arXiv2018

Multiple-Access Channel with Independent Sources: Error Exponent Analysis

In this paper, an achievable error exponent for the multiple-access channel with two independent sources is derived. For each user, the source messages are partitioned into two classes and codebooks are generated by drawing codewords from an input distribution depending on the class index of the source message. The partitioning thresholds that maximize the achievable exponent are given by the solution of a system of equations. We also derive both lower and upper bounds for the achievable exponent in terms of Gallager's source and channel functions. Finally, a numerical example shows that using the proposed ensemble gives a noticeable gain in terms of exponent with respect to independent identically distributed codebooks.

cs.IT↗

arXiv2017

Mismatched Multi-Letter Successive Decoding for the Multiple-Access Channel

This paper studies channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative decoding metric is considered, and achievable rate regions and error exponents are derived both for the standard MAC (independent codebooks), and for the cognitive MAC (one user knows both messages) with superposition coding. In the cognitive case, the rate region and error exponent are shown to be tight with respect to the ensemble average. The rate regions are compared with those of the commonly-considered decoder that chooses the message pair maximizing the decoding metric, and numerical examples are given for which successive decoding yields a strictly higher sum rate for a given pair of input distributions.

cs.IT↗

arXiv2016

Multi-Class Source-Channel Coding

This paper studies an almost-lossless source-channel coding scheme in which source messages are assigned to different classes and encoded with a channel code that depends on the class index. The code performance is analyzed by means of random-coding error exponents and validated by simulation of a low-complexity implementation using existing source and channel codes. While each class code can be seen as a concatenation of a source code and a channel code, the overall performance improves on that of separate source-channel coding and approaches that of joint source-channel coding when the number of classes increases.

cs.IT↗

arXiv2016

Multiuser Random Coding Techniques for Mismatched Decoding

This paper studies multiuser random coding techniques for channel coding with a given (possibly suboptimal) decoding rule. For the mismatched discrete memoryless multiple-access channel, an error exponent is obtained that is tight with respect to the ensemble average, and positive within the interior of Lapidoth's achievable rate region. This exponent proves the ensemble tightness of the exponent of Liu and Hughes in the case of maximum-likelihood decoding. An equivalent dual form of Lapidoth's achievable rate region is given, and the latter is shown to extend immediately to channels with infinite and continuous alphabets. In the setting of single-user mismatched decoding, similar analysis techniques are applied to a refined version of superposition coding, which is shown to achieve rates at least as high as standard superposition coding for any set of random-coding parameters.

cs.IT↗

arXiv2016

Bayesian M-ary Hypothesis Testing: The Meta-Converse and Verdú-Han Bounds are Tight

Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy, Poor and Verdú; the second expression is function of an information-spectrum measure and implies the tightness of a generalized Verdú-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose.

cs.IT↗

arXiv2015

A Counter-Example to the Mismatched Decoding Converse for Binary-Input Discrete Memoryless Channels

This paper studies the mismatched decoding problem for binary-input discrete memoryless channels. An example is provided for which an achievable rate based on superposition coding exceeds the LM rate (Hui, 1983; Csiszár-Körner, 1981), thus providing a counter-example to a previously reported converse result (Balakirsky, 1995). Both numerical evaluations and theoretical results are used in establishing this claim.

cs.IT↗

arXiv2014

Second-Order Rate Region of Constant-Composition Codes for the Multiple-Access Channel

This paper studies the second-order asymptotics of coding rates for the discrete memoryless multiple-access channel with a fixed target error probability. Using constant-composition random coding, coded time-sharing, and a variant of Hoeffding's combinatorial central limit theorem, an inner bound on the set of locally achievable second-order coding rates is given for each point on the boundary of the capacity region. It is shown that the inner bound for constant-composition random coding includes that recovered by i.i.d. random coding, and that the inclusion may be strict. The inner bound is extended to the Gaussian multiple-access channel via an increasingly fine quantization of the inputs.

cs.IT↗

arXiv2014

Expurgated Random-Coding Ensembles: Exponents, Refinements and Connections

This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and non-asymptotic bounds on the error probability for an arbitrary codeword distribution. A simple non-asymptotic bound is shown to attain an exponent of Csiszár and Körner under constant-composition coding. Using Lagrange duality, this exponent is expressed in several forms, one of which is shown to permit a direct derivation via cost-constrained coding which extends to infinite and continuous alphabets. The method of type class enumeration is studied, and it is shown that this approach can yield improved exponents and better tightness guarantees for some codeword distributions. A generalization of this approach is shown to provide a multi-letter exponent which extends immediately to channels with memory. Finally, a refined analysis expurgated i.i.d. random coding is shown to yield a O\big(\frac{1}{\sqrt{n}}\big) prefactor, thus improving on the standard O(1) prefactor. Moreover, the implied constant is explicitly characterized.

cs.IT↗