L. V. Toth - UMR CNRS 7239

L. V. Toth
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L. V. Toth

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Mathematics - Number Theory (23)
Astrophysics of Galaxies (11)
Mathematics - Group Theory (8)
Mathematics - Combinatorics (7)
Quantum Physics (6)
High Energy Astrophysical Phenomena (5)
Solar and Stellar Astrophysics (4)
Physics - Mesoscopic Systems and Quantum Hall Effect (3)
Physics - Materials Science (2)
Cosmology and Nongalactic Astrophysics (2)
General Relativity and Quantum Cosmology (2)
Instrumentation and Methods for Astrophysics (2)
Physics - Superconductivity (2)
Computer Science - Cryptography and Security (2)
Computer Science - Data Structures and Algorithms (1)
Computer Science - Computation and Language (1)
Physics - Data Analysis; Statistics and Probability (1)
Physics - Optics (1)

Publications Authored By L. V. Toth

The work of Braginsky introduced radiation pressure dynamical backaction, in which a mechanical oscillator that is parametrically coupled to an electromagnetic mode can experience a change in its rigidity and its damping rate. The finite cavity electromagnetic decay rate can lead to either amplification or cooling of the mechanical oscillator, and lead in particular to a parametric oscillatory instability, associated with regenerative oscillations of the mechanical oscillator, an effect limiting the circulating power in laser gravitational wave interferometers. These effects implicitly rely on an electromagnetic cavity whose dissipation rate vastly exceeds that of the mechanical oscillator, a condition naturally satisfied in most optomechanical systems. Read More

The formation of deuterated molecules is favoured at low temperatures and high densities. Therefore, the deuteration fraction D$_{frac}$ is expected to be enhanced in cold, dense prestellar cores and to decrease after protostellar birth. Previous studies have shown that the deuterated forms of species such as N2H+ (formed in the gas phase) and CH3OH (formed on grain surfaces) can be used as evolutionary indicators and to constrain their dominant formation processes and time-scales. Read More

We introduce new analogues of the Ramanujan sums, denoted by $\widetilde{c}_q(n)$, associated to unitary divisors, and obtain results concerning the expansions of arithmetic functions of several variables with respect to the sums $\widetilde{c}_q(n)$. We apply these results to certain functions associated with $\sigma^*(n)$ and $\phi^*(n)$, representing the unitary sigma function and unitary phi function, respectively. Read More

Directional amplifiers are an important resource in quantum information processing, as they protect sensitive quantum systems from excess noise. Here, we propose an implementation of phase-preserving and phase-sensitive directional amplifiers for microwave signals in an electromechanical setup comprising two microwave cavities and two mechanical resonators. We show that both can reach their respective quantum limits on added noise. Read More

We generalize certain recent results of Ushiroya concerning Ramanujan expansions of arithmetic functions of two variables. We also show that several properties on expansions of arithmetic functions of one and several variables using classical and unitary Ramanujan sums, respectively, run parallel. Read More

Let $\tau(n)$ be the number of divisors of $n$. We give an elementary proof of the fact that $$ \sum_{n\le x} \tau(n)^r =xC_{r} (\log x)^{2^r-1}+O(x(\log x)^{2^r-2}), $$ for any integer $r\ge 2$. Here, $$ C_{r}=\frac{1}{(2^r-1)!} \prod_{p\ge 2}\left( \left(1-\frac{1}{p}\right)^{2^r} \left(\sum_{\alpha\ge 0} \frac{(\alpha+1)^r}{p^{\alpha}}\right)\right). Read More

Filaments are key for star formation models. As part of the study carried out by the Herschel GCC Programme, here we study the filament properties presented in GCC.VII in context with theoretical models of filament formation and evolution. Read More

Devices that achieve nonreciprocal microwave transmission are ubiquitous in radar and radio-frequency communication systems, and commonly rely on magnetically biased ferrite materials. Such devices are also indispensable in the readout chains of superconducting quantum circuits as they protect sensitive quantum systems from the noise emitted by readout electronics. Since ferrite-based nonreciprocal devices are bulky, lossy, and require large magnetic fields, there has been significant interest in magnetic-field-free on-chip alternatives, such as those recently implemented using Josephson junctions. Read More

We observed thirteen Planck cold clumps with the James Clerk Maxwell Telescope/SCUBA-2 and with the Nobeyama 45 m radio telescope. The N$_2$H$^+$ distribution obtained with the Nobeyama telescope is quite similar to SCUBA-2 dust distribution. The 82 GHz HC$_3$N, 82 GHz CCS, and 94 GHz CCS emission are often distributed differently with respect to the N$_2$H$^+$ emission. Read More

We deduce direct formulas for the total number of subgroups and the number of subgroups of a given order of the group $\Bbb{Z}_m\times \Bbb{Z}_n \times \Bbb{Z}_r \times \Bbb{Z}_s$, where $m,n,r,s\in \Bbb{N}$. The proofs are by some simple group theoretical and number theoretical arguments based on Goursat's lemma for groups. Two conjectures are also formulated. Read More

Recently, attempts have been made to remove Gaussian mixture models (GMM) from the training process of deep neural network-based hidden Markov models (HMM/DNN). For the GMM-free training of a HMM/DNN hybrid we have to solve two problems, namely the initial alignment of the frame-level state labels and the creation of context-dependent states. Although flat-start training via iteratively realigning and retraining the DNN using a frame-level error function is viable, it is quite cumbersome. Read More

We deduce asymptotic formulas for the alternating sums $\sum_{n\le x} (-1)^{n-1} f(n)$ and $\sum_{n\le x} (-1)^{n-1} \frac1{f(n)}$, where $f$ is one of the following classical multiplicative arithmetic functions: Euler's totient function, the Dedekind function, the sum-of-divisors function, the divisor function, the gcd-sum function. We also consider analogs of these functions, which are associated to unitary and exponential divisors, and other special functions. Some of our results improve the error terms obtained by Bordell\`{e}s and Cloitre. Read More

We observed 146 Galactic clumps in HCN (4-3) and CS (7-6) with the Atacama Submillimeter Telescope Experiment (ASTE) 10-m telescope. A tight linear relationship between star formation rate and gas mass traced by dust continuum emission was found for both Galactic clumps and the high redshift (z>1) star forming galaxies (SFGs), indicating a constant gas depletion time of ~100 Myr for molecular gas in both Galactic clumps and high z SFGs. However, low z galaxies do not follow this relation and seem to have a longer global gas depletion time. Read More

We deduce an asymptotic formula with error term for the sum $\sum_{n_1,\ldots,n_k \le x} f([n_1,\ldots, n_k])$, where $[n_1,\ldots, n_k]$ stands for the least common multiple of the positive integers $n_1,\ldots, n_k$ ($k\ge 2$) and $f$ belongs to a large class of multiplicative arithmetic functions, including, among others, the functions $f(n)=n^r$, $\varphi(n)^r$, $\sigma(n)^r$ ($r>-1$ real), where $\varphi$ is Euler's totient function and $\sigma$ is the sum-of-divisors function. The proof is by elementary arguments, using the extension of the convolution method for arithmetic functions of several variables, starting with the observation that given a multiplicative function $f$, the function of $k$ variables $f([n_1,\ldots,n_k])$ is multiplicative. Read More

The Fermi collaboration identified a possible electromagnetic counterpart of the gravitational wave event of September 14, 2015. Our goal is to provide an unsupervised data analysis algorithm to identify similar events in Fermi's Gamma-ray Burst Monitor CTTE data stream. We are looking for signals that are typically weak. Read More

We observed high S/N, high velocity resolution NH$_3$(1,1) and (2,2) emission on an extended map in TMC-1, a filamentary cloud in a nearby quiescent star forming area. By fitting multiple hyperfine-split line profiles to the NH$_3$(1,1) spectra we derived the velocity distribution of the line components and calculated gas parameters on several positions. Herschel SPIRE continuum observations were reduced and used to calculate the physical parameters of the Planck Galactic Cold Clumps in the region. Read More

Previous studies of the initial conditions of massive star formation have mainly targeted Infrared-Dark Clouds (IRDCs) toward the inner Galaxy. This is due to the fact that IRDCs were first detected in absorption against the bright mid-IR background, requiring a favourable location to be observed. By selection, IRDCs represent only a fraction of the Galactic clouds capable of forming massive stars and star clusters. Read More

We explored the AllWISE catalogue of the Wide-field Infrared Survey Explorer mission and identified Young Stellar Object candidates. Reliable 2MASS and WISE photometric data combined with Planck dust opacity values were used to build our dataset and to find the best classification scheme. A sophisticated statistical method, the Support Vector Machine (SVM) is used to analyse the multi-dimensional data space and to remove source types identified as contaminants (extragalactic sources, main sequence stars, evolved stars and sources related to the interstellar medium). Read More

Isolation of a system from its environment is often desirable, from precision measurements to control of individual quantum systems; however, dissipation can also be a useful resource. Remarkably, engineered dissipation enables the preparation of quantum states of atoms, ions or superconducting qubits as well as their stabilization. This is achieved by a suitably engineered coupling to a dissipative cold reservoir formed by electromagnetic modes. Read More

We propose a device architecture capable of direct quantum electro-optical conversion of microwave to optical photons. The hybrid system consists of a planar superconducting microwave circuit coupled to an integrated whispering-gallery-mode microresonator made from an electro-optical material. We show that electro-optical (vacuum) coupling rates $g_0$ as large as$\sim 2\pi \, \mathcal{O}(10-100)$ kHz are achievable with currently available technology, due to the small mode volume of the planar microwave resonator. Read More

We introduce some new higher dimensional generalizations of the Dedekind sums associated with the Bernoulli functions and of those Hardy sums which are defined by the sawtooth function. We generalize a variant of Parseval's formula for the discrete Fourier transform to derive finite trigonometric representations for these sums in a simple unified manner. We also consider a related sum involving the Hurwitz zeta function. Read More

Let $r\ge k\ge 2$ be fixed positive integers. Let $\varrho_{r,k}$ denote the characteristic function of the set of $r$-tuples of positive integers with $k$-wise relatively prime components, that is any $k$ of them are relatively prime. We use the convolution method to establish an asymptotic formula for the sum $\sum_{n_1,\ldots,n_r\le x} \varrho_{r,k}(n_1,\ldots,n_r)$ by elementary arguments. Read More

Several large structures, including the Sloan Great Wall, the Huge Large Quasar Group, and a large gamma-ray burst cluster referred to as the Hercules-Corona Borealis Great Wall, appear to exceed the maximum structural size predicted by Universal inflationary models. The existence of very large structures such as these might necessitate cosmological model modifications. Gamma-ray bursts are the most luminous sources found in nature. Read More

We studied the unbiased optical brightness distribution which was calculated from the survival analysis of host galaxies and its relationship with the Swift GRB data of the host galaxies observed by the Keck telescopes. Based on the sample obtained from merging the Swift GRB table and the Keck optical data we also studied the dependence of this distribution on the data of the GRBs. Finally, we compared the HGs distribution with standard galaxies distribution which is in the DEEP2 galaxies catalog. Read More

Swift's remarkable ability to quickly localize gamma-ray bursts has led to the accumulation of a sizable burst sample for which both angular locations and redshifts are measured. This sample has become large enough that it can potentially be used to probe angular anisotropies indicative of large-scale universal structure. In a previous work, a large clustering of gamma-ray bursts at redshift z about 2 was reported in the general direction of the constellations of Hercules and Corona Borealis. Read More

Universal hashing, discovered by Carter and Wegman in 1979, has many important applications in computer science. MMH$^*$, which was shown to be $\Delta$-universal by Halevi and Krawczyk in 1997, is a well-known universal hash function family. We introduce a variant of MMH$^*$, that we call GRDH, where we use an arbitrary integer $n>1$ instead of prime $p$ and let the keys $\mathbf{x}=\langle x_1, \ldots, x_k \rangle \in \mathbb{Z}_n^k$ satisfy the conditions $\gcd(x_i,n)=t_i$ ($1\leq i\leq k$), where $t_1,\ldots,t_k$ are given positive divisors of $n$. Read More

This paper deals with the number of subgroups of a given exponent in a finite abelian group. Explicit formulas are obtained in the case of rank two and rank three abelian groups. An asymptotic formula is also presented. Read More

According to the cosmological principle, Universal large-scale structure is homogeneous and isotropic. The observable Universe, however, shows complex structures even on very large scales. The recent discoveries of structures significantly exceeding the transition scale of 370 Mpc pose a challenge to the cosmological principle. Read More

In this paper, using properties of Ramanujan sums and of the discrete Fourier transform of arithmetic functions, we give an explicit formula for the number of solutions of the linear congruence $a_1x_1+\cdots +a_kx_k\equiv b \pmod{n}$, with $\gcd(x_i,n)=t_i$ ($1\leq i\leq k$), where $a_1,t_1,\ldots,a_k,t_k, b,n$ ($n\geq 1$) are arbitrary integers. As a consequence, we derive necessary and sufficient conditions under which the above restricted linear congruence has no solutions. The number of solutions of this kind of congruence was first considered by Rademacher in 1925 and Brauer in 1926, in the special case of $a_i=t_i=1$ $(1\leq i \leq k)$. Read More

For every integer $n\ge 1$ let $a_n$ be the smallest positive integer such that $n+a_n$ is prime. We investigate the behavior of the sequence $(a_n)_{n\ge 1}$, and prove asymptotic results for the sums $\sum_{n\le x} a_n$, $\sum_{n\le x} 1/a_n$ and $\sum_{n\le x} \log a_n$. Read More

The project Galactic Cold Cores has made Herschel observations of interstellar clouds where the Planck satellite survey has located cold and compact clumps. The sources range from starless clumps to protostellar cores. We examine 116 Herschel fields to estimate the submillimetre dust opacity and its variations. Read More

The physical and chemical properties of prestellar cores, especially massive ones, are still far from being well understood due to the lack of a large sample. The low dust temperature ($<$14 K) of Planck cold clumps makes them promising candidates for prestellar objects or for sources at the very initial stages of protostellar collapse. We have been conducting a series of observations toward Planck cold clumps (PCCs) with ground-based radio telescopes. Read More

In this work recently produced and commercially available glazed ceramic object with metallic lustre decoration was studied by using a spectroscopic ellipsometer with rotating compensator. The thickness and metal content of the surface lustre layers are determined by ion beam analytical techniques, i.e. Read More

We introduce and study the concept of cyclicity degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. Read More

Let $N_k(n,r,\boldsymbol{a})$ denote the number of incongruent solutions of the quadratic congruence $a_1x_1^2+\ldots+a_kx_k^2\equiv n$ (mod $r$), where $\boldsymbol{a}=(a_1,\ldots,a_k)\in {\Bbb Z}^k$, $n\in {\Bbb Z}$, $r\in {\Bbb N}$. We give short direct proofs for certain less known compact formulas on $N_k(n,r,\boldsymbol{a})$, valid for $r$ odd, which go back to the work of Minkowski, Bachmann and Cohen. We also deduce some other related identities and asymptotic formulas which do not seem to appear in the literature. Read More

In this paper we introduce and study a family $\Phi_k$ of arithmetic functions generalizing Euler's totient function. These functions are given by the number of solutions to the equation $\gcd(x_1^2+\ldots +x_k^2, n)=1$ with $x_1,\ldots,x_k \in {\mathbb{Z}}/n{\mathbb{Z}}$ which, for $k=2,4$ and $8$ coincide, respectively, with the number of units in the rings of Gaussian integers, quaternions and octonions over ${\mathbb{Z}}/n{\mathbb{Z}}$. We prove that $\Phi_k$ is multiplicative for every $k$, we obtain an explicit formula for $\Phi_k(n)$ in terms of the prime-power decomposition of $n$ and derive an asymptotic formula for $\sum_{n\le x} \Phi_k(n)$. Read More

L1642 is one of the two high galactic latitude (|b| > 30deg) clouds confirmed to have active star formation. We examine the properties of this cloud, especially the large-scale structure, dust properties, and compact sources in different stages of star formation. We present high-resolution far-infrared and submm observations with the Herschel and AKARI satellites and mm observations with the AzTEC/ASTE telescope, which we combined with archive data from near- and mid-infrared (2MASS, WISE) to mm observations (Planck). Read More

Using Goursat's lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group Z_m x Z_n are deduced, where m and n are arbitrary positive integers. As consequences, explicit formulas for the total number of subgroups, the number of subgroups with a given invariant factor decomposition, and the number of subgroups of a given order are obtained. Read More

We survey general properties of multiplicative arithmetic functions of several variables and related convolutions, including the Dirichlet convolution and the unitary convolution. We introduce and investigate a new convolution, called gcd convolution. We define and study the convolutes of arithmetic functions of several variables, according to the different types of convolutions. Read More

We demonstrate the use of the AKARI survey photometric data in the study of galactic star formation. Our aim was to select young stellar objects (YSOs) in the AKARI FIS catalogue. We used AKARI Far-Infrared Surveyor and Wide-field Infrared Survey Explorer data to derive mid- and far-infrared colours of YSOs. Read More

The Rosette complex is a well studied region of the galactic plane which presents the apparent characteristics of a triggered star forming region. This is however still debated as no strong evidence corroborates this statement. We focus on characterizing the young stellar population in the Rosette complex to improve our understanding of the processes that regulate the star formation in this region. Read More

Let $\Z_m$ be the group of residue classes modulo $m$. Let $s(m,n)$ and $c(m,n)$ denote the total number of subgroups of the group $\Z_m \times \Z_n$ and the number of its cyclic subgroups, respectively, where $m$ and $n$ are arbitrary positive integers. We derive asymptotic formulas for the sums $\sum_{m,n\le x} s(m,n)$, $\sum_{m,n\le x} c(m,n)$ and for the corresponding sums restricted to $\gcd(m,n)>1$, i. Read More

We investigate an arithmetic function representing a generalization of the gcd-sum function, considered by Kurokawa and Ochiai in 2009 in connection with the multivariable global Igusa zeta function for a finite cyclic group. We show that the asymptotic properties of this function are closely connected to the Piltz divisor function. A generalization of Menon's identity is also considered. Read More

We give a simple proof and a multivariable generalization of an identity due to E. Alkan concerning a weighted average of the Ramanujan sums. We deduce identities for other weighted averages of the Ramanujan sums with weights concerning logarithms, values of arithmetic functions for gcd's, the Gamma function, the Bernoulli polynomials, and binomial coefficients. Read More

We describe the subgroups of the group $\Z_m \times \Z_n \times \Z_r$ and derive a simple formula for the total number $s(m,n,r)$ of the subgroups, where $m,n,r$ are arbitrary positive integers. An asymptotic formula for the function $n\mapsto s(n,n,n)$ is also deduced. Read More

An integer $k$ is called regular (mod $n$) if there exists an integer $x$ such that $k^2x\equiv k$ (mod $n$). This holds true if and only if $k$ possesses a weak order (mod $n$), i.e. Read More

We derive two new generalizations of the Busche-Ramanujan identities involving the multiple Dirichlet convolution of arithmetic functions of several variables. The proofs use formal multiple Dirichlet series and properties of symmetric polynomials of several variables. Read More

We deduce a simple representation and the invariant factor decompositions of the subgroups of the group $\Bbb{Z}_m \times \Bbb{Z}_n$, where $m$ and $n$ are arbitrary positive integers. We obtain formulas for the total number of subgroups and the number of subgroups of a given order. Read More

In this review paper, we survey the main concepts and some of the recent developments in quantum feedback control. For consistency and clarity, essential ideas and notations in the theory of open quantum systems and quantum stochastic calculus, as well as continuous measurement theory are developed. We give a general description of quantum feedback control, set up a coherent model and compare it to open-loop designs. Read More

Affiliations: 1GPM, 2GPM, 3UMR CNRS 7239, 4UMR CNRS 7239, 5UMR CNRS 7239, 6UMR CNRS 7239, 7UMR CNRS 7239

The combined strengthening effects of grain refinement and high precipitated volume fraction (~6at.%) on the mechanical properties of FeSiTi alloy subjected to SPD processing prior to aging treatment were investigated by atom probe tomography and scanning transmission electron microscopy. It was shown that the refinement of the microstructure affects the precipitation kinetics and the spatial distribution of the secondary hardening intermetallic phase, which was observed to nucleate heterogeneously on dislocations and sub-grain boundaries. Read More