arXiv subjects

J. Camacho

Publications and source records attributed to J. Camacho.

At least 19 recordsLinked to original sources

arXiv2026

Bridging local and semilocal stability: A topological approach

This paper establishes a general topological condition under which the semilocal stability of a set-valued mapping can be exactly determined by its local stability properties. Specifically, we investigate the relationship between the Lipschitz upper semicontinuity modulus -- a semilocal measure of variation for the image set -- and the local calmness moduli. While these two quantities coincide for mappings with convex graphs, the relationship generally breaks down in the absence of convexity, making the semilocal modulus exceptionally difficult to compute. We prove that if a mapping is outer semicontinuous in the Painlev\'{e}-Kuratowski sense and locally compact around the nominal parameter, the Lipschitz upper semicontinuity modulus is exactly the supremum of the local calmness moduli over the nominal set. In addition to the theoretical advance, this equality enables the precise calculation of semilocal error bounds via point-based formulae. We illustrate the broad applicability of this theorem by setting it up in several non-convex frameworks in parametric optimization, including piecewise convex and semi-algebraic mappings, feasible and optimal set mappings under full data perturbations, generalized equations and linear complementarity problems, semi-infinite inequality systems, and parameterized sub-level sets.

math.OC↗

arXiv2023

Feasibility problems via paramonotone operators in a convex setting

This paper is focused on some properties of paramonotone operators on Banach spaces and their application to certain feasibility problems for convex sets in a Hilbert space and convex systems in the Euclidean space. In particular, it shows that operators that are simultaneously paramonotone and bimonotone are constant on their domains, and this fact is applied to tackle two particular situations. The first one, closely related to simultaneous projections, deals with a finite amount of convex sets with an empty intersection and tackles the problem of finding the smallest perturbations (in the sense of translations) of these sets to reach a nonempty intersection. The second is focused on the distance to feasibility; specifically, given an inconsistent convex inequality system, our goal is to compute/estimate the smallest right-hand side perturbations that reach feasibility. We advance that this work derives lower and upper estimates of such a distance, which become the exact value when confined to linear systems.

math.OC↗

arXiv2023

Hoffman constant of the argmin mapping in linear optimization

The main goal of this paper is to provide a point-based expression for the Hoffman constant of the argmin mapping in linear optimization, understood as the sharp Lipschitz constant restricted to its domain. The work is mainly developed in the parametric context of right-hand side perturbations of the constraint system. To the authors' knowledge, this is the first exact formula for this constant, although we can find in the literature different upper estimates. The paper tackles this objective from a broader perspective, which introduces new tools of their own interest, such as the concept of well-connected piecewise convex mapping. We isolate the nice behavior of such mappings to derive a crucial equality between the Hoffman constant (which is a global stability measure) and the supremum of calmness moduli (of local nature). The paper also includes some specifics about directional stability of optimal solutions and finishes with some conclusions and notes about further research.

math.OC↗

arXiv2019

All Sparse PCA Models Are Wrong, But Some Are Useful. Part I: Computation of Scores, Residuals and Explained Variance

Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When moving from PCA to sPCA, there are a number of implications that the practitioner needs to be aware of. A relevant one is that scores and loadings in sPCA may not be orthogonal. For this reason, the traditional way of computing scores, residuals and variance explained that is used in the classical PCA cannot directly be applied to sPCA models. This also affects how sPCA components should be visualized. In this paper we illustrate this problem both theoretically and numerically using simulations for several state-of-the-art sPCA algorithms, and provide proper computation of the different elements mentioned. We show that sPCA approaches present disparate and limited performance when modeling noise-free, sparse data. In a follow-up paper, we discuss the theoretical properties that lead to this problem.

stat.ML↗

arXiv2016

First principles Kinetic-Collective thermal conductivity of semiconductors

A fully predictive Kinetic Collective Model using first principles phonon spectra and relaxation times is presented. Thermal conductivity values obtained for Si, Ge, C (diamond) and GaAs in a wide range of sizes and temperatures have good agreement with experimental data without the use of any fitting parameter. This validation of the model open the door to discuss how the precise combination of kinetic and collective contributions to heat transport could provide a useful framework to interpret recent complex experiments displaying non-Fourier behavior.

cond-mat.mtrl-sci↗

arXiv2014

Monte Carlo simulations of post-common-envelope white dwarf + main sequence binaries: The effects of including recombination energy

Detached WD+MS PCEBs are perhaps the most suitable objects for testing predictions of close-compact binary-star evolution theories, in particular, CE evolution. The population of WD+MS PCEBs has been simulated by several authors in the past and compared with observations. However, most of those predictions did not take the possible contributions to the envelope ejection from additional sources of energy (mostly recombination energy) into account. Here we update existing binary population models of WD+MS PCEBs by assuming that a fraction of the recombination energy available within the envelope contributes to ejecting the envelope. We performed Monte Carlo simulations of 10^7 MS+MS binaries for 9 different models using standard assumptions for the initial primary mass function, binary separations, and initial-mass-ratio distribution and evolved these systems using the publicly available BSE code. Including a fraction of recombination energy leads to a clear prediction of a large number of long orbital period (>~10 days) systems mostly containing high-mass WDs. The fraction of systems with He-core WD primaries increases with the CE efficiency and the existence of very low-mass He WDs is only predicted for high values of the CE efficiency (>~0.5). All models predict on average longer orbital periods for PCEBs containing C/O-core WDs than for PCEBs containing He WDs. This effect increases with increasing values of both efficiencies. Longer periods after the CE phase are also predicted for systems containing more massive secondary stars. The initial-mass-ratio distribution affects the distribution of orbital periods, especially the distribution of secondary star masses. Our simulations, in combination with a large and homogeneous observational sample, can provide constraints on the values of the CE efficiencies, as well as on the initial-mass-ratio distribution for MS+MS binary stars.

astro-ph.SR↗

arXiv2014

Monte Carlo simulations of post-common-envelope white dwarf + main sequence binaries: comparison with the SDSS DR7 observed sample

Detached white dwarf + main sequence (WD+MS) systems represent the simplest population of post-common envelope binaries (PCEBs). Since the ensemble properties of this population carries important information about the characteristics of the common-envelope (CE) phase, it deserves close scrutiny. However, most population synthesis studies do not fully take into account the effects of the observational selection biases of the samples used to compare with the theoretical simulations. Here we present the results of a set of detailed Monte Carlo simulations of the population of WD+MS binaries in the Sloan Digital Sky Survey (SDSS) Data Release 7. We used up-to-date stellar evolutionary models, a complete treatment of the Roche lobe overflow episode, and a full implementation of the orbital evolution of the binary systems. Moreover, in our treatment we took into account the selection criteria and all the known observational biases. Our population synthesis study allowed us to make a meaningful comparison with the available observational data. In particular, we examined the CE efficiency, the possible contribution of internal energy, and the initial mass ratio distribution (IMRD) of the binary systems. We found that our simulations correctly reproduce the properties of the observed distribution of WD+MS PCEBs. In particular, we found that once the observational biases are carefully taken into account, the distribution of orbital periods and of masses of the WD and MS stars can be correctly reproduced for several choices of the free parameters and different IMRDs, although models in which a moderate fraction (<=10%) of the internal energy is used to eject the CE and in which a low value of CE efficiency is used (<=0.3) seem to fit better the observational data. We also found that systems with He-core WDs are over-represented in the observed sample, due to selection effects.

astro-ph.GA↗

arXiv2013

Scarcity may promote cooperation in populations of simple agents

In the study of the evolution of cooperation, resource limitations are usually assumed just to provide a finite population size. Recently, however, it has been pointed out that resource limitation may also generate dynamical payoffs able to modify the original structure of the games. Here we study analytically a phase transition from a homogeneous population of defectors when resources are abundant to the survival of unconditional cooperators when resources reduce below a threshold. To this end, we introduce a model of simple agents, with no memory or ability of recognition, interacting in well-mixed populations. The result might shed light on the role played by resource constraints on the origin of multicellularity.

physics.bio-ph↗

arXiv2012

On the origin of high-field magnetic white dwarfs

High-field magnetic white dwarfs have been long suspected to be the result of stellar mergers. However, the nature of the coalescing stars and the precise mechanism that produces the magnetic field are still unknown. Here we show that the hot, convective, differentially rotating corona present in the outer layers of the remnant of the merger of two degenerate cores is able to produce magnetic fields of the required strength that do not decay for long timescales. We also show, using an state-of-the-art Monte Carlo simulator, that the expected number of high-field magnetic white dwarfs produced in this way is consistent with that found in the solar neighborhood.

astro-ph.SR↗

arXiv2012

Double degenerate mergers as progenitors of high-field magnetic white dwarfs

astro-ph.SR↗

arXiv2011

The white dwarf cooling sequence of NGC 6791: a unique tool for stellar evolution

NGC 6791 is a well-studied, metal-rich open cluster that is so close to us that can be imaged down to luminosities fainter than that of the termination of its white dwarf cooling sequence, thus allowing for an in-depth study of its white dwarf population. We use a Monte Carlo simulator that employs up-to-date evolutionary cooling sequences for white dwarfs with hydrogen-rich and hydrogen-deficient atmospheres, with carbon-oxygen and helium cores. The cooling sequences for carbon-oxygen cores account for the delays introduced by both Ne^22 sedimentation in the liquid phase and by carbon-oxygen phase separation upon crystallization. We do not find evidence for a substantial fraction of helium-core white dwarfs, and hence our results support the suggestion that the origin of the bright peak of the white dwarf luminosity function can only be attributed to a population of unresolved binary white dwarfs. Moreover, our results indicate that the number distribution of secondary masses of the population of unresolved binaries has to increase with increasing mass ratio between the secondary and primary components of the progenitor system. We also find that the observed cooling sequence appears to be able to constrain the presence of progenitor sub-populations with different chemical compositions and the fraction of non-DA white dwarfs. Our simulations place interesting constraints on important characteristics of the stellar populations of NGC 6791. In particular, we find that the fraction of single helium-core white dwarfs must be smaller than 5%, that a sub-population of stars with zero metallicity must be <12%, while if the adopted metallicity of the sub-population is solar the upper limit is ~8%. Finally, we also find that the fraction of non-DA white dwarfs in this particular cluster is surprinsingly small <6%.

astro-ph.SR↗

arXiv2011

Electronic structure of superconducting KC$_8$ and non-superconducting LiC$_6$ graphite intercalation compounds: Evidence for a graphene-sheet-driven superconducting state

We have performed photoemission studies of the electronic structure in LiC$_6$ and KC$_8$, a non-superconducting and a superconducting graphite intercalation compound, respectively. We have found that the charge transfer from the intercalant layers to graphene layers is larger in KC$_8$ than in LiC$_6$, opposite of what might be expected from their chemical composition. We have also measured the strength of the electron-phonon interaction on the graphene-derived Fermi surface to carbon derived phonons in both materials and found that it follows a universal trend where the coupling strength and superconductivity monotonically increase with the filling of graphene $π^{\ast}$ states. This correlation suggests that both graphene-derived electrons and graphene-derived phonons are crucial for superconductivity in graphite intercalation compounds.

cond-mat.supr-con↗

arXiv2011

The experimental observation of quantum Hall effect of l = 3 chiral charge carriers in trilayer graphene

Low-energy electronic states in monolayer and bilayer graphenes present chiral charge carriers with unique and unusual properties of interest for electronic applications. Here, we report the magnetotransport measurements in the ABC-stacked trilayer graphene as a function of charge carrier density, magnetic field, and temperature, which show clear evidence of l = 3 chiral quasiparticles with cubic dispersion, existing in a large, 20x60 sq. microns device. Shubnikov-deHaas oscillations (SdHO) reveal the Berry's phase 3π, and the marked increase of cyclotron mass near charge neutrality, consistent with divergent behavior expected for l = 3 quasiparticles. We also observe the predicted unconventional sequence of quantum Hall effect (QHE) plateaus, +/-6e^2/h, +/-10e^2/h, ... .

cond-mat.str-el↗

arXiv2010

Einstein Modes in the Phonon Density of States of the Single-Filled Skutterudite Yb$_{0.2}$Co$_{4}$Sb$_{12}$

Measurements of the phonon density of states by inelastic neutron \emph{time-of-flight} scattering and specific heat measurements along with first principles calculations, provide compelling evidence for the existence of an Einstein oscillator ("\emph{rattler}") at $ω_{E1} \approx$ 5.0 meV in the filled skutterudite Yb$_{0.2}$Co$_{4}$Sb$_{12}$. Multiple dispersionless modes in the measured density of states of Yb$_{0.2}$Co$_{4}$Sb$_{12}$ at intermediate transfer energies (14 meV $\leq$ \emph{$ω$} $\leq$ 20 meV) are exhibited in both the experimental and theoretical \emph{density-of-states} of the Yb-filled specimen. A peak at 12.4 meV is shown to coincide with a second Einstein mode at \emph{$ω_{E2} \approx$} 12.8 meV obtained from heat capacity data. The local modes at intermediate transfer energies are attributed to altered properties of the host CoSb$_{3}$ cage as a result of Yb-filling. It is suggested that these modes are owed to a complementary mechanism for the scattering of heat-carrying phonons in addition to the mode observed at $ω_{E1} \, \approx$ 5.0 meV. Our observations offer a plausible explanation for the significantly-higher \textit{dimensionless figures of merit} of filled skutterudites, compared to their parent compounds.

cond-mat.mtrl-sci↗

arXiv2010

White dwarfs with hydrogen-deficient atmospheres and the dark matter content of the Galaxy

The nature of the several microlensing events observed by the MACHO team towards the Large Magellanic Cloud (LMC) is still a subject of debate. Low-mass substellar objects and stars with masses larger than ~M_{sun} have been ruled out as major components of a Massive Astrophysical Compact Halo Object (MACHO) Galactic halo, while stars of half a solar mass seem to be viable candidates. Main sequence stars have been already discarded, and there are tight restrictions on the role played by white dwarfs with hydrogen-dominated atmospheres. In this paper we evaluate the contribution to the dark matter content of the Galaxy of white dwarfs with hydrogen-deficient atmospheres. For this purpose we use a Monte Carlo simulator which incorporates up-to-date evolutionary sequences of white dwarfs with hydrogen-rich and hydrogen-deficient atmospheres. We also take into account detailed descriptions of the thick disk and the halo of our Galaxy as well as of a reliable model of the LMC. We find that the contribution of white dwarfs with hydrogen-deficient atmospheres moderately increases the theoretical estimate of the optical depth with respect to the value obtained when only hydrogen-rich white dwarfs are considered. We also find that the contribuiton of the thick disk population of white dwarfs is comparable to the halo contribution. However, the contributions of both the halo and the thick disk white-dwarf populations are still insufficient to explain the number of events observed by the MACHO team. Finally, we find that the contribution to the halo dark matter of the entire population under study is less than 10% at the 95% conficence level.

astro-ph.GA↗

arXiv2009

Breakdown of the N=0 Quantum Hall State in graphene: two insulating regimes

We studied the unusual Quantum Hall Effect (QHE) near the charge neutrality point (CNP) in high-mobility graphene sample for magnetic fields up to 18 T. We observe breakdown of the delocalized QHE transport and strong increase in resistivities $ρ_{xx},|ρ_{xy}|$ with decreasing Landau level filling for $ν< 2$, where we identify two insulating regimes. For $1 \gtrsim |ν| \gtrsim 1/2$ we find an exponential increase of $ρ_{xx,xy} \sim e^{a(H-H_c)}$ within the range up to several resistance quanta $R_K$, while the Hall effect gradually disappears, consistent with the Hall insulator (HI) with local transport. Then, at $ν\approx 1/2$ a cusp in $ρ_{xx}(H)$ followed by an onset of even faster growth indicates transition to a collective insulator (CI) state. The likely candidate for this state is a pinned Wigner crystal.

cond-mat.mes-hall↗

arXiv2008

The contribution of red dwarfs and white dwarfs to the halo dark matter

The nature of the several microlensing events observed by the MACHO team towards the LMC still remains controversial. Low-mass substellar objects and stars with masses larger than ~1 M_{sun} have been ruled out as major components of a MACHO galactic halo, while stars of half solar masses are the most probable candidates. In this paper we assess jointly the relative contributions of both red dwarfs and white dwarfs to the mass budget of the galactic halo. In doing so we use a Monte Carlo simulator which incorporates up-to-date evolutionary sequences of both red dwarfs and white dwarfs as well as detailed descriptions of our Galaxy and of the LMC. We explore the complete mass range between 0.08 and 1 M_{sun} as possible microlensing candidates and we compare the synthetic populations obtained with our simulator with the results obtained by the MACHO and EROS experiments. Our results indicate that, despite that the contribution of the red dwarf population increases by a factor of 2 the value of the optical depth obtained when taking into account the white dwarf population alone, it is still insufficient to explain the number of events claimed by the MACHO team. Finally, we find that the contribution to the halo dark matter of the whole population under study is smaller than 10% at the 95% conficence level.

astro-ph↗

arXiv2008

Anisotropic Electron-Phonon Coupling and Dynamical Nesting on the Graphene Sheets in CaC6

Superconductivity in graphite intercalated compounds has been studied for more than 40 years and it is still not fully understood, despite the recent progress and the discovery of relatively high Tc superconductivity in CaC6 and YbC6. Recent studies now suggest that the electron-phonon coupling is most likely responsible for pairing and that the intercalant-derived electronic states and vibrations play the dominant role. Here, we present the first studies of electronic structure in CaC6, a superconductor with Tc=11.6 K. Using angle-resolved photoemission spectroscopy, we find that, contrary to theoretical models, the EPC on the graphene-derived Fermi sheets is surprisingly strong, reflecting the interaction with high-frequency graphene-derived vibrations. Thus, in addition to the amazing properties in the charge-neutral state, graphene sheets also show surprises in the heavily doped regime: they may support strong pairing interactions and lead to superconductivity in compounds in which they are building blocks.

cond-mat.supr-con↗