arXiv subjects
Publications and source records attributed to Abhishek Pandey.
In this paper, the concept of Riemannian warped product submersion is generalized to the conformal case. We introduce the notion of conformal warped product submersion. It is a submersion between warped product manifolds that preserves angles between the horizontal vectors. The fundamental tensors of submersion are derived for conformal warped product submersion.
Let $\mathcal{S}$ denote the class of analytic and univalent ({\it i.e.}, one-to-one) functions $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$ in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$. For $f\in \mathcal{S}$, Ma proposed the generalized Zalcman conjecture that $$|a_{n}a_{m}-a_{n+m-1}|\le (n-1)(m-1),\,\,\,\mbox{ for } n\ge2,\, m\ge 2,$$ with equality only for the Koebe function $k(z) = z/(1 - z)^2$ and its rotations. In this paper using the properties of holomorphic motion and Krushkal's Surgery Lemma \cite{Krushkal-1995}, we prove the generalized Zalcman conjecture when $n=2$, $m=3$ and $n=2$, $m=4$.
Let $\mathcal{A}$ denote the class of analytic functions in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$ satisfying $f(0)=0$ and $f'(0)=1$. Let $\mathcal{U}$ be the class of functions $f\in\mathcal{A}$ satisfying $$\left|f'(z)\left(\frac{z}{f(z)}\right)^2-1 \right|< 1 \quad\mbox{ for } z\in\mathbb{D},$$ and $\mathscr{G}$ denote the class of functions $f\in \mathcal{A}$ satisfying $${\rm Re\,}\left(1+\frac{zf''(z)}{f'(z)}\right)>-\frac{1}{2} \quad\mbox{ for } z\in\mathbb{D}.$$
Automatic Speech Recognition (ASR) systems suffer considerably when source speech is corrupted with noise or room impulse responses (RIR). Typically, speech enhancement is applied in both mismatched and matched scenario training and testing. In matched setting, acoustic model (AM) is trained on dereverberated far-field features while in mismatched setting, AM is fixed. In recent past, mapping speech features from far-field to close-talk using denoising autoencoder (DA) has been explored. In this paper, we focus on matched scenario training and show that the proposed joint VAE based mapping achieves a significant improvement over DA. Specifically, we observe an absolute improvement of 2.5% in word error rate (WER) compared to DA based enhancement and 3.96% compared to AM trained directly on far-field filterbank features.
Training a robust Automatic Speech Recognition (ASR) system for children's speech recognition is a challenging task due to inherent differences in acoustic attributes of adult and child speech and scarcity of publicly available children's speech dataset. In this paper, a novel segmental spectrum warping and perturbations in formant energy are introduced, to generate a children-like speech spectrum from that of an adult's speech spectrum. Then, this modified adult spectrum is used as augmented data to improve end-to-end ASR systems for children's speech recognition. The proposed data augmentation methods give 6.5% and 6.1% relative reduction in WER on children dev and test sets respectively, compared to the vocal tract length perturbation (VTLP) baseline system trained on Librispeech 100 hours adult speech dataset. When children's speech data is added in training with Librispeech set, it gives a 3.7 % and 5.1% relative reduction in WER, compared to the VTLP baseline system.
High-quality single crystals of KCo$_2$As$_2$ with the body-centered tetragonal ThCr$_2$Si$_2$ structure were grown using KAs self flux. Structural, magnetic, thermal, and electrical transport were investigated. No clear evidence for any phase transitions was found in the temperature range 2 to 300 K. The in-plane electrical resistivity $ρ$ versus temperature $T$ is highly unusual, showing a $T^4$ behavior below 30 K and an anomalous positive curvature up to 300 K which is different from the linear behavior expected from the Bloch-Grüneisen theory for electron scattering by acoustic phonons. This positive curvature has been previously observed in the in-plane resistivity of high-conductivity layered delafossites such as PdCoO$_2$ and PtCoO$_2$. The in-plane $ρ(T\to0) = 0.36~μΩ$ cm of KCo$_2$As$_2$ is exceptionally small for this class of compounds. The material also exhibits a nearly linear magnetoresistance at low $T$ which attains a value of about 40% at $T=2$K and magnetic field $H= 80$ kOe. The magnetic susceptibility $χ$ of KCo$_2$As$_2$ is isotropic and about an order of magnitude smaller than the values for the related compounds SrCo$_2$As$_2$ and BaCo$_2$As$_2$. The $χ$ increases above 100 K which is found from our first-principles calculations to arise from a sharp peak in the electronic density of states just above the Fermi energy $E_{\rm F}$. Heat capacity $C_{\rm p}(T)$ data at low $T$ yield an electronic density of states $N(E_{\rm F})$ that is about 36% larger than predicted by the first-principles theory. The $C_{\rm p}(T)$ data near room temperature suggest the presence of excited optic vibration modes which may also be the source of the positive curvature in $ρ(T)$. Our results show that KCo$_2$As$_2$ provides a new avenue for investigating the physics of high-purity metals.
Conventional automatic speech recognition (ASR) system uses second-order minkowski loss during inference time which is suboptimal as it incorporates only first order statistics in posterior estimation [2]. In this paper we have proposed higher order minkowski loss (4th Order and 6th Order) during inference time, without any changes during training time. The main contribution of the paper is to show that higher order loss uses higher order statistics in posterior estimation, which improves the prediction ability of acoustic model in ASR system. We have shown mathematically that posterior probability obtained due to higher order loss is function of second order posterior and thus the method can be incorporated in standard ASR system in an easy manner. It is to be noted that all changes are proposed during test(inference) time, we do not make any change in any training pipeline. Multiple baseline systems namely, TDNN1, TDNN2, DNN and LSTM are developed to verify the improvement incurred due to higher order minkowski loss. All experiments are conducted on LibriSpeech dataset and performance metrics are word error rate (WER) on "dev-clean", "test-clean", "dev-other" and "test-other" datasets.
This paper presents a novel deep learning architecture for acoustic model in the context of Automatic Speech Recognition (ASR), termed as MixNet. Besides the conventional layers, such as fully connected layers in DNN-HMM and memory cells in LSTM-HMM, the model uses two additional layers based on Mixture of Experts (MoE). The first MoE layer operating at the input is based on pre-defined broad phonetic classes and the second layer operating at the penultimate layer is based on automatically learned acoustic classes. In natural speech, overlap in distribution across different acoustic classes is inevitable, which leads to inter-class mis-classification. The ASR accuracy is expected to improve if the conventional architecture of acoustic model is modified to make them more suitable to account for such overlaps. MixNet is developed keeping this in mind. Analysis conducted by means of scatter diagram verifies that MoE indeed improves the separation between classes that translates to better ASR accuracy. Experiments are conducted on a large vocabulary ASR task which show that the proposed architecture provides 13.6% and 10.0% relative reduction in word error rates compared to the conventional models, namely, DNN and LSTM respectively, trained using sMBR criteria. In comparison to an existing method developed for phone-classification (by Eigen et al), our proposed method yields a significant improvement.
We carried out $^{75}$As nuclear magnetic resonance (NMR) measurements on the trigonal CaMn$_2$As$_2$ and SrMn$_2$As$_2$ insulators exhibiting antiferromagnetic (AFM) ordered states below Néel temperatures $T_{\rm N}$ = 62 K and 120 K, respectively. In the paramagnetic state above $T_{\rm N}$, typical quadrupolar-split $^{75}$As-NMR spectra were observed for both systems. The $^{75}$As quadrupolar frequency $ν_{\rm Q}$ for CaMn$_2$As$_2$ decreases with decreasing temperature, while $ν_{\rm Q}$ for SrMn$_2$As$_2$ increases, showing an opposite temperature dependence.In the AFM state, the relatively sharp and distinct $^{75}$As NMR lines were observed in SrMn$_2$As$_2$ and the NMR spectra were shifted to lower fields for both magnetic fields $H$ $||$ $c$ axis and $H$ $||$ $ab$ plane, suggesting that the internal fields $B_{\rm int}$ at the As site produced by the Mn ordered moments are nearly perpendicular to the external magnetic field direction. No obvious distribution of $B_{\rm int}$ was observed in SrMn$_2$As$_2$, which clearly indicates a commensurate AFM state. In sharp contrast to SrMn$_2$As$_2$, broad and complex NMR spectra were observed in CaMn$_2$As$_2$ in the AFM state, which clearly shows a distribution of $B_{\rm int}$ at the As site, indicating an incommensurate state. From the analysis of the characteristic shape of the observed spectra, the AFM state of CaMn$_2$As$_2$ was determined to be a two-dimensional incommensurate state where Mn ordered moments are aligned in the $ab$ plane. A possible origin for the different AFM states in the systems was discussed. Both CaMn$_2$As$_2$ and SrMn$_2$As$_2$ show very large anisotropy in the nuclear spin-lattice relaxation rate 1/$T_1$ in the paramagnetic state. 1/$T_1$ for $H$ $||$ $ab$ is much larger than that for $H$ $|| $c$, indicating strong anisotropic AFM spin fluctuations in both compounds.
We present a comprehensive study of the low-energy band structure and Fermi surface (FS) topology of $A$Co$_2$As$_2$ ($A=$ Ca, Sr, Ba, Eu) using high-resolution angle-resolved photoemission spectroscopy. The experimental FS topology and band dispersion data are compared with theoretical full-potential linearized augmented-plane-wave (FP-LAPW) calculations, which yielded reasonably good agreement. We demonstrate that the FS maps of $A$Co$_2$As$_2$ are significantly different from those of the parent compounds of Fe-based high-temperature superconductors. Further, the FSs of CaCo$_2$As$_2$ do not show significant changes across its antiferromagnetic transition temperature. The band dispersions extracted in different momentum $(k_{\it x}, k_{\it y})$ directions show a small electron pocket at the center and a large electron pocket at the corner of the Brillouin zone (BZ). The absence of the hole FS in these compounds does not allow nesting between pockets at the Fermi energy ({\it E}$_{\rm F}$), which is in contrast to $A$Fe$_2$As$_2$-type parent compounds of the iron-based superconductors. Interestingly, we find that the hole bands are moved 300--400~meV below $E_{\rm F}$ depending on the $A$ element. Moreover, the existence of nearly flat bands in the vicinity of $E_{\rm F}$ are consistent with the large density of states at $E_{\rm F}$. These results are important to understand the physical properties as well as the possibility of the emergence of superconductivity in related materials.
Fabrication and characterization of instrument for high-temperature simultaneous measurement of Seebeck coefficient (S) and thermal conductivity ($κ$) has been carried out with python automation. The steady-state based Fourier's law of thermal conduction is employed for $κ$ measurement. The parallel thermal conductance technique is implemented for heat loss measurement. Introducing the thin heater and insulating heater base minimize the heat loss and make the way easier to arrive at high temperature. Measurement of S is carried out using differential method. Same thermocouples are used to measure temperature as well as voltage for S measurement. Care of temperature dependent S of thermocouple has also been taken. Simple design, small size, lightweightmake this instrument more robust. All the components for making sample holder are easily available in the market and can be replaced as per the user demand. This instrument can measure samples with various dimensions and shapes in the temperature range 300 $-$ 800 K. The instrument is validated using different class of samples, such as nickel, gadolinium, Fe$_{2}$VAl and LaCoO$_{3}$. Wide range of S from $\sim$ $-$20 to $\sim$600 $μ$V/K and $κ$ from $\sim$1.1 to $\sim$23.5 W/m-K are studied. The measured values of S and k are in good agreement with the reported data.
The COVID-19 pandemic has resulted in more than 125 million infections and more than 2.7 million casualties. In this paper, we attempt to classify covid vs non-covid cough sounds using signal processing and deep learning methods. Air turbulence, the vibration of tissues, movement of fluid through airways, opening, and closure of glottis are some of the causes for the production of the acoustic sound signals during cough. Does the COVID-19 alter the acoustic characteristics of breath, cough, and speech sounds produced through the respiratory system? This is an open question waiting for answers. In this paper, we incorporated novel data augmentation methods for cough sound augmentation and multiple deep neural network architectures and methods along with handcrafted features. Our proposed system gives 14% absolute improvement in area under the curve (AUC). The proposed system is developed as part of Interspeech 2021 special sessions and challenges viz. diagnosing of COVID-19 using acoustics (DiCOVA). Our proposed method secured the 5th position on the leaderboard among 29 participants.
Let $\mathcal{A}$ denote the class of analytic functions in the unit disk $\mathbb{D}$ of the form $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$ and $\mathcal{S}$ denote the class of functions $f\in\mathcal{A}$ which are univalent ({\it i.e.}, one-to-one). In 1960s, L. Zalcman conjectured that $|a_n^2-a_{2n-1}|\le (n-1)^2$ for $n\ge 2$, which implies the famous Bieberbach conjecture $|a_n|\le n$ for $n\ge 2$. For $f\in \mathcal{S}$, Ma \cite{Ma-1999} proposed a generalized Zalcman conjecture $$|a_{n}a_{m}-a_{n+m-1}|\le (n-1)(m-1) $$ for $n\ge 2, m\ge 2$. Let $\mathcal{U}$ be the class of functions $f\in\mathcal{A}$ satisfying $$ \left|f'(z)\left(\frac{z}{f(z)}\right)^2-1 \right|< 1 \quad\mbox{ for } z\in\mathbb{D}. $$ and $\mathcal{F}$ denote the class of functions $f\in \mathcal{A}$ satisfying ${\rm Re\,}(1-z)^{2}f'(z)>0$ in $\mathbb{D}$. In the present paper, we prove the Zalcman conjecture and generalized Zalcman conjecture for the class $\mathcal{U}$ using extreme point theory. We also prove the Zalcman conjecture and generalized Zalcman conjecture for the class $\mathcal{F}$ for the initial coefficients.
The novel coronavirus disease (COVID-19) pandemic has resulted in over 200,000 cases in India. Thus far, India has implemented lockdown measures to curb disease transmission. However, commercial sex work in red-light areas (RLAs) has potential to lead to COVID-19 resurgence after lockdown. We developed a model of COVID-19 transmission in RLAs, evaluating the impact of extended RLA closure compared with RLA reopening on cases, hospitalizations, and mortality rates within the RLAs of five major Indian cities, within the cities, and across India. Closure lowered transmission at all scales. More than 90% of cumulative cases and deaths among RLA residents of Kolkata, Pune, and Nagpur could be averted by the time the epidemic would peak under a re-opening scenario. Across India, extended closure of RLAs would benefit the population at large, delaying the peak of COVID-19 cases by 8 to 23 days, and avert 32% to 60.2% of cumulative cases and 43% to 67.6% of cumulative deaths at the peak of the epidemic. Extended closure of RLAs until better prevention and treatment strategies are developed would benefit public health in India.
We have recently proposed a deterministic matrix dynamics at the Planck scale, for gravity coupled to Dirac fermions, evolving in the so-called Connes time. By coarse-graining this dynamics over time intervals much larger than Planck time, we derived the space-time manifold, quantum theory, and classical general relativity, as low energy emergent approximations to the underlying matrix dynamics. In the present article, we show how to include Yang-Mills gauge fields in this Planck scale matrix dynamics. We do this by appropriately modifying the fundamental action for the previously introduced `atom' of space-time-matter [which we now call an `aikyon']. This is achieved by modifying the Dirac operator to include a `potential' for the Yang-Mills aspect, and a `current' for the Yang-Mills charge. Our work opens up an avenue for unification of gravity with gauge-fields and Dirac fermions. We show how spontaneous localisation in the matrix dynamics gives rise to general relativity coupled to gauge-fields and relativistic point particles, in the classical limit. We use this formalism to explain the remarkable fact that the Kerr-Newman black hole has the same value for the gyromagnetic ratio as that for a Dirac fermion, both being twice the classical value.
We report investigations of the structural, magnetic, electrical transport and thermal properties of five compositions of the metallic perovskite GdRh$_3$C$_{1-x}$B$_x$ ($0.00 \le x \le 1.00$). Our results show that all the five compositions undergo magnetic ordering at low temperatures, but the nature of the ordered state is significantly different in the carbon- and the boron-rich compositions, where the former shows signatures of an amplitude-modulated magnetic structure and the latter exhibits evidences of an equal-moment incommensurate antiferromagnetic ordering. We also observe a remarkable field-dependent evolution of conduction carrier polarization in the compositionally disordered compounds. The outcomes indicate that this system is energetically situated in proximity to a magnetic instability where small variations in the control parameter(s), such as lattice constant and/or electron density, lead to considerably different ground states.
We report measurements on Ti$_4$MnBi$_2$, where a crystal structure involving linear chains of Mn ions suggests one-dimensional magnetic character. The electrical resistivity is metallic, consistent with the results of electronic structure calculations that find a robust Fermi surface albeit with moderate electronic correlations. Curie-Weiss fit to the magnetic susceptibility finds that the Mn moments are in the low-spin $S = 1/2$ configuration. Neutron diffraction measurements detect weak antiferromagnetic order within the Mn chains, with further evidence for the small staggered moment coming from the entropy associated with the ordering peak in the specific heat as well as from the results of spin-polarized electronic structure calculations. The antiferromagnetic moments are apparently associated with the $d_{x^{2}-y^{2}}$ and $d_{xy}$ orbitals of Mn while the remaining Mn orbitals are delocalized. Strong quantum fluctuations, possibly related to an electronic instability that forms the Mn moment or to the one-dimensional character of Ti$_4$MnBi$_2$, nearly overcome magnetic order.
We report the synthesis and properties of a new layered tetragonal ternary compound CsMn$_4$As$_3$ (structure: KCu$_4$S$_3$-type, space group: $P4/mmm$, No. 123 and $Z = 2$). The material is a small band-gap semiconductor and exhibits an antiferromagnetic ground state associated with Mn spins. The compound exhibits a signature of a distinct magnetic moment canting event at 150(5)~K with a canting angle of $\approx 0.3^{\circ}$. Although, some features of the magnetic characteristics of this new compound are qualitatively similar to those of the related BaMn$_2$As$_2$, the underlying Mn sublattices of the two materials are quite different. While the Mn square-lattice layers in BaMn$_2$As$_2$ are equally spaced along the $c$-direction with the interlayer distance $d_{\rm L\,Ba} = 6.7341(4)$ Ang., the Mn sublattice forms bilayers in CsMn$_4$As$_3$ with the interlayer distance within a bilayer $d_{\rm L\,Cs} = 3.1661(6)$ Ang. and the distance between the two adjacent bilayers $d_{\rm B} = 7.290(6)$ Ang. This difference in the Mn sublattice is bound to significantly alter the energy balance between the $J_{1}$, $J_{2}$ and $J_{c}$ exchange interactions within the J1-J2-Jc model compared to that in BaMn$_2$As$_2$ and the other related 122 compounds including the well-known iron-arsenide superconductor parent compound BaFe$_2$As$_2$. Owing to the novelty of its transition metal sublattice, this new addition to the family of tetragonal materials related to the iron-based superconductors brings prospects for doping and pressure studies in the search of new superconducting phases as well as other exciting correlated-electron properties.