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A crack free and high structural quality Sr2Nb2O7 single crystals were grown by the optical float zone method using optimized growth parameters. Laue pattern confirms single crystalline nature of the grown crystal. Temperature dependent Raman and Brillouin light scattering studies reveal a significant shift in phonon modes across normal to incommensurate phase transition (Tn-in) which occurs ~ 488 K. In the temperature range from 900 down to 500 K, two optical phonon modes about 63 (B1 mode) and 54 cm-1 (A1 mode) were observed. The frequency of A1 mode strongly decreases with an increase in temperature above the Tn-in while the frequency of this mode almost remains constant below the Tn-in. In contrast the frequency of B1 phonon mode is found to increase with temperature in the range of 500 - 900 K but it does not display a significant shift below the phase transition temperature. In addition in the incommensurate phase a new optical phonon mode at 35 cm-1 also begins to appear and exhibits strong stiffening behavior with increase in temperature in the range of 300 - 488 K. Moreover, the anomalous behavior of the acoustic phonon across Tn-in were further probed using Brilliouin scattering. Longitudinal acoustic phonon mode at 41 GHz exhibits strong change in slope near Tn-in. In addition, the transverse acoustic modes at 28.6 and 22.4 GHz also exhibit strong anomalies with minimum in frequency near Tn-in. The inelastic light scattering studies provide valuable information on the phase transition., Comment: 12 pages, 8 figures

It is well known that descents and excedances are equidistributed in the symmetric group. We show that the descent and excedance enumerators, summed over permutations with a fixed first letter are identical when we perform a simple change of the first letter. We generalize this to type B and other colored permutation groups. We are led to defining descents and excedances through linear orders. With respect to a particular order, when the number of colors is even, we get a result that generalizes the type B results. Lastly, we get a type B counterpart of Conger's result which refines the well known Carlitz identity., Comment: 14 pages

Ultrasound fetal imaging is beneficial to support prenatal development because it is affordable and non-intrusive. Nevertheless, fetal plane classification (FPC) remains challenging and time-consuming for obstetricians since it depends on nuanced clinical aspects, which increases the difficulty in identifying relevant features of the fetal anatomy. Thus, to assist with its accurate feature extraction, a lightweight artificial intelligence architecture leveraging convolutional neural networks and attention mechanisms is proposed to classify the largest benchmark ultrasound dataset. The approach fine-tunes from lightweight EfficientNet feature extraction backbones pre-trained on the ImageNet1k. to classify key fetal planes such as the brain, femur, thorax, cervix, and abdomen. Our methodology incorporates the attention mechanism to refine features and 3-layer perceptrons for classification, achieving superior performance with the highest Top-1 accuracy of 96.25%, Top-2 accuracy of 99.80% and F1-Score of 0.9576. Importantly, the model has 40x fewer trainable parameters than existing benchmark ensemble or transformer pipelines, facilitating easy deployment on edge devices to help clinical practitioners with real-time FPC. The findings are also interpreted using GradCAM to carry out clinical correlation to aid doctors with diagnostics and improve treatment plans for expectant mothers., Comment: Submitted to Computers in Biology and Medicine journal

Skin diseases affect over a third of the global population, yet their impact is often underestimated. Automating skin disease classification to assist doctors with their prognosis might be difficult. Nevertheless, due to efficient feature extraction pipelines, deep learning techniques have shown much promise for various tasks, including dermatological disease identification. This study uses a skin disease dataset with 31 classes and compares it with all versions of Vision Transformers, Swin Transformers and DivoV2. The analysis is also extended to compare with benchmark convolution-based architecture presented in the literature. Transfer learning with ImageNet1k weights on the skin disease dataset contributes to a high test accuracy of 96.48\% and an F1-Score of 0.9727 using DinoV2, which is almost a 10\% improvement over this data's current benchmark results. The performance of DinoV2 was also compared for the HAM10000 and Dermnet datasets to test the model's robustness, and the trained model overcomes the benchmark results by a slight margin in test accuracy and in F1-Score on the 23 and 7 class datasets. The results are substantiated using explainable AI frameworks like GradCAM and SHAP, which provide precise image locations to map the disease, assisting dermatologists in early detection, prompt prognosis, and treatment., Comment: Submitted to Computers in Biology and Medicine

Unimodality of the normalized coefficients of the characteristic polynomial of distance matrices of trees are known and bounds on the location of its peak (the largest coefficient) are also known. Recently, an extension of these results to distance matrices of block graphs was given. In this work, we extend these results to two additional distance-type matrices associated with trees: the Min-4PC matrix and the 2-Steiner distance matrix. We show that the sequences of coefficients of the characteristic polynomials of these matrices are both unimodal and log-concave. Moreover, we find the peak location for the coefficients of the characteristic polynomials of the Min-4PC matrix of any tree on $n$ vertices. Further, we show that the Min-4PC matrix of any tree on $n$ vertices is isometrically embeddable in $\mathbb{R}^{n-1}$ equipped with the $\ell_1$ norm.

Reifegerste and independently, Petersen and Tenner studied a statistic $\mathrm{drops}()$ on permutations in $\mathfrak{S}_n$. Two other studied statistics on $\mathfrak{S}_n$ are $\mathrm{depth}$ and $\mathrm{exc}$. Using descents in ${\it canonical\ reduced\ words}$ of elements in $\mathfrak{S}_n$, we give an involution $f_A: \mathfrak{S}_n \mapsto \mathfrak{S}_n$ that leads to a neat formula for the signed trivariate enumerator of $\mathrm{drops},\mathrm{depth}, \mathrm{exc}$ in $\mathfrak{S}_n$. This gives a simple formula for the signed univariate drops enumerator in $\mathfrak{S}_n$. For the type-B Coxeter group $\mathfrak{B}_n$ as well, using similar techniques, we show analogous results. For the type D Coxeter group, we again get analogous results, but our proof is inductive. Under the famous Foata-Zeilberger bijection $\phi_{FZ}$ which takes permutations to restricted Laguerre histories, we show that permutations $\pi$ and $f_A(\pi)$ map to the same Motzkin path, but have different history components. Using the Foata-Zeilberger bijection, we also get a continued fraction for the generating function enumerating the pair of statistics $\mathrm{drops}$ and $\mathrm{MAD}$. Graham and Diaconis determined the mean and the variance of the Spearman metric of disarray $D(\pi)$ when one samples $\pi$ from $\mathfrak{S}_n$ at random. As an application of our results, we get the mean and variance of the statistic $\mathrm{drops}(\pi)$ when we sample $\pi$ from $\mathcal{A}_n$ at random., Comment: 24 pages, 3 figures. Comments are welcome!

Deep networks tend to learn spurious feature-label correlations in real-world supervised learning tasks. This vulnerability is aggravated in distillation, where a student model may have lesser representational capacity than the corresponding teacher model. Often, knowledge of specific spurious correlations is used to reweight instances & rebalance the learning process. We propose a novel early readout mechanism whereby we attempt to predict the label using representations from earlier network layers. We show that these early readouts automatically identify problem instances or groups in the form of confident, incorrect predictions. Leveraging these signals to modulate the distillation loss on an instance level allows us to substantially improve not only group fairness measures across benchmark datasets, but also overall accuracy of the student model. We also provide secondary analyses that bring insight into the role of feature learning in supervision and distillation.

$\newcommand{\Max}{\mathrm{Max4PC}}$ The Four point condition (4PC henceforth) is a well known condition characterising distances in trees $T$. Let $w,x,y,z$ be four vertices in $T$ and let $d_{x,y}$ denote the distance between vertices $x,y$ in $T$. The 4PC condition says that among the three terms $d_{w,x} + d_{y,z}$, $d_{w,y} + d_{x,z}$ and $d_{w,z} + d_{x,y}$ the maximum value equals the second maximum value. We define an $\binom{n}{2} \times \binom{n}{2}$ sized matrix $\Max_T$ from a tree $T$ where the rows and columns are indexed by size-2 subsets. The entry of $\Max_T$ corresponding to the row indexed by $\{w,x\}$ and column $\{y,z\}$ is the maximum value among the three terms $d_{w,x} + d_{y,z}$, $d_{w,y} + d_{x,z}$ and $d_{w,z} + d_{x,y}$. In this work, we determine basic properties of this matrix like rank, give an algorithm that outputs a family of bases, and find the determinant of $\Max_T$ when restricted to our basis. We further determine the inertia and the Smith Normal Form (SNF) of $\Max_T$.

Let $T$ be a tree on $n$ vertices and let $L_q^T$ be the $q$-analogue of its Laplacian. For a partition $\lambda \vdash n$, let the normalized immanant of $L_q^T$ indexed by $\lambda$ be denoted as $d_{\lambda}(L_q^T)$. A string of inequalities among $d_{\lambda}(L_q^T)$ is known when $\lambda$ varies over hook partitions of $n$ as the size of the first part of $\lambda$ decreases. In this work, we show a similar sequence of inequalities when $\lambda$ varies over two row partitions of $n$ as the size of the first part of $\lambda$ decreases. Our main lemma is an identity involving binomial coefficients and irreducible character values of $S_n$ indexed by two row partitions. Our proof can be interpreted using the combinatorics of Riordan paths and our main lemma admits a nice probabilisitic interpretation involving peaks at odd heights in generalized Dyck paths or equivalently involving special descents in Standard Young Tableaux with two rows. As a corollary, we also get inequalities between $d_{\lambda_1}(L_q^{T_1})$ and $d_{\lambda_2}(L_q^{T_2})$ when $T_1$ and $T_2$ are comparable trees in the $GTS_n$ poset and when $\lambda_1$ and $\lambda_2$ are both two rowed partitions of $n$, with $\lambda_1$ having a larger first part than $\lambda_2$.

Carlitz and Scoville in 1973 considered a four variable polynomial that enumerates permutations in $\mathfrak{S}_n$ with respect to the parity of its descents and ascents. In recent work, Pan and Zeng proved a $q$-analogue of Carlitz-Scoville's generating function by enumerating permutations with the above four statistice along with the inversion number. Further, they also proved a type B analogue by enumerating signed permutations with respect to the parity of descents and ascents. In this work we prove a $q$-analogue of the type B result of Pan and Zeng by enumerating permutations in $\mathfrak{B}_n$ with the above four statistics and the type B inversion number. We also obtain a $q$-analogue of the generating function for the type B bivariate alternating descent polynomials. We consider a similar five-variable polynomial in the type D Coxeter groups as well and give their egf. Alternating descents for the type D groups were previously also defined by Remmel, but our definition is slightly different. As a by-product of our proofs, we get bivariate $q$-analogues of Hyatt's recurrences for the type B and type D Eulerian polynomials. Further corollaries of our results are some symmetry relations for these polynomials and $q$-analogues of generating functions for snakes of types B and D., Comment: 27 pages. Comments are welcome

Training state-of-the-art ASR systems such as RNN-T often has a high associated financial and environmental cost. Training with a subset of training data could mitigate this problem if the subset selected could achieve on-par performance with training with the entire dataset. Although there are many data subset selection(DSS) algorithms, direct application to the RNN-T is difficult, especially the DSS algorithms that are adaptive and use learning dynamics such as gradients, as RNN-T tend to have gradients with a significantly larger memory footprint. In this paper, we propose Partitioned Gradient Matching (PGM) a novel distributable DSS algorithm, suitable for massive datasets like those used to train RNN-T. Through extensive experiments on Librispeech 100H and Librispeech 960H, we show that PGM achieves between 3x to 6x speedup with only a very small accuracy degradation (under 1% absolute WER difference). In addition, we demonstrate similar results for PGM even in settings where the training data is corrupted with noise.

In several supervised learning scenarios, auxiliary losses are used in order to introduce additional information or constraints into the supervised learning objective. For instance, knowledge distillation aims to mimic outputs of a powerful teacher model; similarly, in rule-based approaches, weak labeling information is provided by labeling functions which may be noisy rule-based approximations to true labels. We tackle the problem of learning to combine these losses in a principled manner. Our proposal, AMAL, uses a bi-level optimization criterion on validation data to learn optimal mixing weights, at an instance level, over the training data. We describe a meta-learning approach towards solving this bi-level objective and show how it can be applied to different scenarios in supervised learning. Experiments in a number of knowledge distillation and rule-denoising domains show that AMAL provides noticeable gains over competitive baselines in those domains. We empirically analyze our method and share insights into the mechanisms through which it provides performance gains.

Data subset selection from a large number of training instances has been a successful approach toward efficient and cost-effective machine learning. However, models trained on a smaller subset may show poor generalization ability. In this paper, our goal is to design an algorithm for selecting a subset of the training data, so that the model can be trained quickly, without significantly sacrificing on accuracy. More specifically, we focus on data subset selection for L2 regularized regression problems and provide a novel problem formulation which seeks to minimize the training loss with respect to both the trainable parameters and the subset of training data, subject to error bounds on the validation set. We tackle this problem using several technical innovations. First, we represent this problem with simplified constraints using the dual of the original training problem and show that the objective of this new representation is a monotone and alpha-submodular function, for a wide variety of modeling choices. Such properties lead us to develop SELCON, an efficient majorization-minimization algorithm for data subset selection, that admits an approximation guarantee even when the training provides an imperfect estimate of the trained model. Finally, our experiments on several datasets show that SELCON trades off accuracy and efficiency more effectively than the current state-of-the-art.

With the goal of making deep learning more label-efficient, a growing number of papers have been studying active learning (AL) for deep models. However, there are a number of issues in the prevalent experimental settings, mainly stemming from a lack of unified implementation and benchmarking. Issues in the current literature include sometimes contradictory observations on the performance of different AL algorithms, unintended exclusion of important generalization approaches such as data augmentation and SGD for optimization, a lack of study of evaluation facets like the labeling efficiency of AL, and little or no clarity on the scenarios in which AL outperforms random sampling (RS). In this work, we present a unified re-implementation of state-of-the-art AL algorithms in the context of image classification via our new open-source AL toolkit DISTIL, and we carefully study these issues as facets of effective evaluation. On the positive side, we show that AL techniques are $2\times$ to $4\times$ more label-efficient compared to RS with the use of data augmentation. Surprisingly, when data augmentation is included, there is no longer a consistent gain in using BADGE, a state-of-the-art approach, over simple uncertainty sampling. We then do a careful analysis of how existing approaches perform with varying amounts of redundancy and number of examples per class. Finally, we provide several insights for AL practitioners to consider in future work, such as the effect of the AL batch size, the effect of initialization, the importance of retraining the model at every round, and other insights., Comment: 10 pages in main paper, 6 figures in main paper, 2 tables in main paper. 24 pages in total, 15 figures in total, 13 tables in total

The great success of modern machine learning models on large datasets is contingent on extensive computational resources with high financial and environmental costs. One way to address this is by extracting subsets that generalize on par with the full data. In this work, we propose a general framework, GRAD-MATCH, which finds subsets that closely match the gradient of the training or validation set. We find such subsets effectively using an orthogonal matching pursuit algorithm. We show rigorous theoretical and convergence guarantees of the proposed algorithm and, through our extensive experiments on real-world datasets, show the effectiveness of our proposed framework. We show that GRAD-MATCH significantly and consistently outperforms several recent data-selection algorithms and achieves the best accuracy-efficiency trade-off. GRAD-MATCH is available as a part of the CORDS toolkit: \url{https://github.com/decile-team/cords}., Comment: To appear in Proceedings of the 38 th International Conference on Machine Learning, PMLR 139, 2021

Large scale machine learning and deep models are extremely data-hungry. Unfortunately, obtaining large amounts of labeled data is expensive, and training state-of-the-art models (with hyperparameter tuning) requires significant computing resources and time. Secondly, real-world data is noisy and imbalanced. As a result, several recent papers try to make the training process more efficient and robust. However, most existing work either focuses on robustness or efficiency, but not both. In this work, we introduce Glister, a GeneraLIzation based data Subset selecTion for Efficient and Robust learning framework. We formulate Glister as a mixed discrete-continuous bi-level optimization problem to select a subset of the training data, which maximizes the log-likelihood on a held-out validation set. Next, we propose an iterative online algorithm Glister-Online, which performs data selection iteratively along with the parameter updates and can be applied to any loss-based learning algorithm. We then show that for a rich class of loss functions including cross-entropy, hinge-loss, squared-loss, and logistic-loss, the inner discrete data selection is an instance of (weakly) submodular optimization, and we analyze conditions for which Glister-Online reduces the validation loss and converges. Finally, we propose Glister-Active, an extension to batch active learning, and we empirically demonstrate the performance of Glister on a wide range of tasks including, (a) data selection to reduce training time, (b) robust learning under label noise and imbalance settings, and (c) batch-active learning with several deep and shallow models. We show that our framework improves upon state of the art both in efficiency and accuracy (in cases (a) and (c)) and is more efficient compared to other state-of-the-art robust learning algorithms in case (b).

The alternating-runs polynomial enumerates alternating runs in the symmetric group. There are three formulae for the number of permutations, $R_{n,k}$ in $\mathfrak{S}_n$ with $k$ alternating runs, but all of them are complicated. We show that when enumerated with sign taken into account, one gets a {\it neat formula}. As a consequence, we get a near refinement of a result of Wilf on the exponent of $(1+t)$ when it divides the alternating-runs polynomial in the alternating group $\mathcal{A}_n$. Other applications include a moment-type identity and enumeration of alternating permutations in $\mathcal{A}_n$. Similar results are obtained for the type B and type D Coxeter groups.

Wilf showed that the the alternating runs polynomial $R_n(t)$ counting the number of permutations in the Symmetric group is divisible by $(1+t)^m$ where $m = \lfloor (n-2)/2 \rfloor$. Recently, B\'{o}na gave a group action based proof. Type B and D analogues of Wilf's result are known. In this note, we extend B\'{o}na's proof to prove the type B and D analogue., Comment: 9 pages. Added a section on applications of this result to refining moment-type identities

Central Limit Theorems are known for the Eulerian statistic "descent" (or "excedance") in the symmetric group $\SSS_n$. Recently, Fulman, Kim, Lee and Petersen gave a Central Limit Theorem for "descent" over the alternating group $\AAA_n$ and also gave a Carlitz identity in $\AAA_n$ using descents. In this paper, we give a Central Limit Theorem in $\AAA_n$ involving excedances. We extend these to the positive elements in type B and type D Coxeter groups. Boroweic and M\l{}otkowski enumerated type B descents over $\DD_n$, the type D Coxeter group and gave similar results. We refine their results for both the positive and negative part of $\DD_n$. Our results are a consequence of signed enumeration over these subsets., Comment: Corrected a wrong spelling of an author "Borowiec". The earlier version mis-spelled all occurrences. Thanks to Prof. M\l{}otkowski for pointing this out

Let $T$ be a tree on $n$ vertices with $q$-Laplacian $L_T^q$ and Laplacian matrix $L_T$. Let $GTS_n$ be the generalized tree shift poset on the set of unlabelled trees on $n$ vertices. Inequalities are known between coefficients of the immanantal polynomial of $L_T$ (and $L_T^q$) as we go up the poset $GTS_n$. Using the Frobenius characteristic, this can be thought as a result involving the schur symmetric function $s_{\lambda}$. In this paper, we use an arbitrary symmetric function to define a {\it generalized matrix function} of an $n \times n$ matrix. When the symmetric function is the monomial and the forgotten symmetric function, we generalize such inequalities among coefficients of the generalized matrix polynomial of $L_T^q$ as we go up the $GTS_n$ poset., Comment: 11 pages

The classical Eulerian polynomials $A_n(t)$ are known to be gamma positive. Define the positive Eulerian polynomial $\mathsf{AExc^{+}}_n(t)$ as the polynomial obtained when we sum excedances over the alternating group. We show that $\mathsf{AExc^{+}}_n(t)$ is gamma positive iff $n \geq 5$ and $n \equiv 1$ (mod 2). When $n \geq 4$, and $n \equiv 0$ (mod 2) we show that $\mathsf{AExc^{+}}_n(t)$ can be written as a sum of two gamma positive polynomials. Similar results are shown when we consider the positive type-D and type-D Eulerian polynomials. Finally, we show gamma positivity results when we sum excedances over derangements with positive and negative sign. Our main resuls is that the polynomial obtained by summing excedance over a conjugacy class indexed by $\lambda$ is gamma positive., Comment: 20 pages. arXiv admin note: text overlap with arXiv:1812.01927

The classical Eulerian polynomials $A_n(t)$ are known to be gamma positive. Define the positive Eulerian polynomial $A_n^+(t)$ as the polynomial obtained when we sum descents over the alternating group. We show that $A_n^+(t)$ is gamma positive iff $n \equiv 0,1$ (mod 4). When $n \equiv 2$ (mod 4) we show that $A_n^+(t)$ can be written as a sum of two gamma positive polynomials while if $n \equiv 3$ (mod 4), we show that $A_n^+(t)$ can be written as a sum of three gamma positive polynomials. Similar results are shown when we consider the positive type-D and type-D Eulerian polynomials., Comment: 24 pages

Let $T$ be a tree on $n$ vertices with Laplacian $L_T$ and let $GTS_n$ be the generalized tree shift poset on the set of unlabelled trees on $n$ vertices. Inequalities are known for coefficients of the characteristic polynomial of $L_T$ as we go up the poset $GTS_n$. In this work, we generalize these inequalities to the $q$-Laplacian $L^q_T$ of $T$ and to the coefficients of all immanantal polynomials.

Bismuth substituted lutetium iron garnet (BLIG) films exhibit larger Faraday rotation, and have a higher Curie temperature than yttrium iron garnet. We have observed magnetic stripe domains and measured domain widths of 1.4 {\mu}{\mu}m using Fourier domain polarization microscopy, Faraday rotation experiments yield a coercive field of 5 Oe. These characterizations form the basis of micromagnetic simulations that allow us to estimate and compare spin wave excitations in BLIG films. We observed that these films support thermal magnons with a precessional frequency of 7 GHz with a line width of 400 MHz. Further, we studied the dependence of precessional frequency on the externally applied magnetic field. Brillouin light scattering experiments and precession frequencies predicted by simulations show similar trend with increasing field., Comment: Journal of Magnetism and Magnetic Materials, 2017

In this paper, we consider the class of strongly bi-close-to-convex functions of order $\alpha$ and bi-close-to-convex functions of order $\beta$. We obtain an upper bound estimate for the second Hankel determinant for functions belonging to these classes. The results in this article improve some earlier result obtained for the class of bi-convex functions.

A rigorous thermodynamic expression is derived for the total biological information capacity per unit length of a DNA molecule. The total information includes the usual four letter coding sequence information plus that excess information coding often erroneously referred to as "junk". We conclude that the currently understood human DNA code is about a hundred megabyte program written on a molecule with about a ten gigabyte memory. By far, most of the programing code is not presently understood., Comment: Two Pages

Brillouin spectroscopic measurements have been carried out on relaxor ferroelectric Pb(Zn1/3Nb2/3)0.85Ti0.15O3 (PZN-PT) single crystal over the temperature range 300-585 K. The longitudinal acoustic phonon begins to soften below 650 K, which is attributed to the Burns temperature (TB). On the other hand, the line width of the longitudinal acoustic (LA) phonon mode exhibits a sharp Landau-Khalatnikov-like maximum and an accompanying anomaly in the LA mode frequency around 463 K, the tetragonal-cubic phase transition temperature (Ttc). In addition, a broad central peak, found below the characteristic intermediate temperature T* ~ 525 K, exhibits critical slowing down upon approaching Ttc indicating an order-disorder nature of the phase transition. The relaxation time of polar nano regions estimated from the broad central peak is found to be same as that obtained for LA phonon mode suggesting an electrostrictive coupling between strain and polarization fluctuations. The activation energy for the PNRs relaxation-dynamics is found to be ~236 meV. Polarized nature of the central peak suggests that the polar nano regions have the tendency to form long-range polar ordering.

This paper is about the wireless sensor network in environmental monitoring applications. A Wireless Sensor Network consists of many sensor nodes and a base station. The number and type of sensor nodes and the design protocols for any wireless sensor network is application specific. The sensor data in this application may be light intensity, temperature, pressure, humidity and their variations .Clustering and routing are the two areas which are given more attention in this paper., Comment: 7 Pages, 2 Figures and 1 Table

Chemical reactions can be induced at a distance due to the propagation of electromagnetic signals during intermediate chemical stages. Although it is well known at optical frequencies, e.g. photosynthetic reactions, electromagnetic signals hold true for much lower frequencies. In E. coli bacteria such electromagnetic signals can be generated by electric transitions between energy levels describing electrons moving around DNA loops. The electromagnetic signals between different bacteria within a community is a "wireless" version of intercellular communication found in bacterial communities connected by "nanowires". The wireless broadcasts can in principle be of both the AM and FM variety due to the magnetic flux periodicity in electron energy spectra in bacterial DNA orbital motions., Comment: four pages and no figures; minor typographical errors fixed

Soft multi-photon radiation from hard higher energy reaction sources can be employed to describe three major well established properties of biophoton radiation; Namely, (i) the mild radiation intensity decreases for higher frequencies, (ii) the coherent state Poisson counting statistics, and (iii) the time delayed luminescence with a hyperbolic time tail. Since the soft photon frequencies span the visible to the ultraviolet frequency range, the hard reaction sources have energies extending into the nuclear transmutation regime., Comment: 5 Pages and 1 figure

This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural controllability, our approach uses an undirected graph: the behavioral approach to modelling dynamical systems allows this. Given a system of linear, constant coefficient, ordinary differential equations of any order, we formulate necessary and sufficient conditions for controllability in terms of weights of the edges in a suitable bipartite graph constructed from % components with equal bipartite cardinality in the differential-algebraic system. % of equations. A key notion that helps formulate the conditions is that of a `redundant edge'. Removal of all redundant edges makes the inferring of structural controllability a straightforward exercise. We use standard graph algorithms as ingredients to check these conditions and hence obtain an algorithm to check for structural controllability. We provide an analysis of the running time of our algorithm. When our results are applied to the familiar state space description of a system, we obtain a novel necessary and sufficient condition to check structural controllability for this description., Comment: 17 pages, 2 figures

Geographic location search engines allow users to constrain and order search results in an intuitive manner by focusing a query on a particular geographic region. Geographic search technology, also called location search, has recently received significant interest from major search engine companies. Academic research in this area has focused primarily on techniques for extracting geographic knowledge from the web. In this paper, we study the problem of efficient query processing in scalable geographic search engines. Query processing is a major bottleneck in standard web search engines, and the main reason for the thousands of machines used by the major engines. Geographic search engine query processing is different in that it requires a combination of text and spatial data processing techniques. We propose several algorithms for efficient query processing in geographic search engines, integrate them into an existing web search query processor, and evaluate them on large sets of real data and query traces., Comment: IEEE Publication format, International Journal of Computer Science and Information Security, IJCSIS, Vol. 8 No. 1, April 2010, USA. ISSN 1947 5500, http://sites.google.com/site/ijcsis/

We consider general theoretical models of water and in particular the nature of the motions of the hydrogen nuclei. If the motion of hydrogen nuclei is classical, then the thermodynamic pressure equation of state for heavy water wherein the hydrogen nuclei are deuterons is identical to the pressure equation of state for light water wherein the hydrogen nuclei are protons. Since the experimental thermodynamic phase diagram for light water is clearly measurably different from the experimental thermodynamic phase diagram for heavy water, one may deduce that the motions of hydrogen nuclei are quantum mechanical in nature. This conclusion is in physical agreement with a recent analysis of X-ray, neutron and deep inelastic neutron scattering data., Comment: ReVTeX 4, 4 pages no figures

The phenomenological equations of motion for the relaxation of ordered phases of magnetized and polarized crystal phases can be developed in close analogy with one another. For the case of magnetized systems, the driving magnetic field intensity toward relaxation was developed by Gilbert. For the case of polarized systems, the driving electric field intensity toward relaxation was developed by Khalatnikov. The transport times for relaxation into thermal equilibrium can be attributed to viscous sound wave damping via magnetostriction for the magnetic case and electrostriction for the polarization case., Comment: 5 pages no figures ReVTeX 4

Efforts aimed at large-scale integration of nanoelectronic devices that exploit the superior electronic and mechanical properties of single-walled carbon nanotubes (SWCNTs) remain limited by the difficulties associated with manipulation and packaging of individual SWNTs. Alternative approaches based on ultra-thin carbon nanotube networks (CNNs) have enjoyed success of late with the realization of several scalable device applications. However, precise control over the network electronic transport is challenging due to i) an often uncontrollable interplay between network coverage and its topology and ii) the inherent electrical heterogeneity of the constituent SWNTs. In this letter, we use template-assisted fluidic assembly of SWCNT networks to explore the effect of geometric confinement on the network topology. Heterogeneous SWCNT networks dip-coated onto sub-micron wide ultra-thin polymer channels exhibit a topology that becomes increasingly aligned with decreasing channel width and thickness. Experimental scale coarse-grained computations of interacting SWCNTs show that the effect is a reflection of an aligned topology that is no longer dependent on the network density, which in turn emerges as a robust knob that can induce semiconductor-to-metallic transitions in the network response. Our study demonstrates the effectiveness of directed assembly on channels with varying degrees of confinement as a simple tool to tailor the conductance of the otherwise heterogeneous network, opening up the possibility of robust large-scale CNN-based devices., Comment: 4 pages, 3 figures

The objective of this paper is to implement the Trie based Tuple Space Search(TTSS) packet classification algorithm for Network Processor(NP) based router to enhance multimedia applications. The performance is evaluated using Intel IXP2400 NP Simulator. The results demonstrate that, TTSS has better performance than Tuple Space Search algorithm and is well suited to achieve high speed packet classification to support multimedia applications., Comment: 6 Pages, International Journal of Computer Science and Information Security (IJCSIS)

1LO optical phonons in free-standing mixed Cd1-xZnxS nanocrystals, synthesized using chemical precipitation, are investigated using Raman spectroscopy. As expected for the nanocrystals, the 1-LO modes are found to appear at slightly lower wavenumbers than those in the bulk mixed crystals and exhibit one mode behavior. On the other hand, the line broadening is found to be much more than that can be accounted on the basis of phonon confinement. From the detailed line shape analysis it turns out that the substitutional disorder in the mixed crystals contributes much more to the line broadening than the phonon confinement. The linewidth arising from these mechanisms are also extracted from the analysis., Comment: 15 Pages,8 Figures, Accepted in J. Raman Spectroscopy

Recent studies of turbulence in superfluid Helium indicate that turbulence in quantum fluids obeys a Kolmogorov scaling law. Such a law was previously attributed to classical solutions of the Navier-Stokes equations of motion. It is suggested that turbulence in all fluids is due to quantum fluid mechanical effects. Employing a field theoretical view of the fluid flow velocity, vorticity appears as quantum filamentary strings. This in turn leads directly to the Kolmogorov critical indices for the case of fully developed turbulence., Comment: ReVTeX4 format, no figures

A cylindrical flexible cable made up of pure fluid water can be experimentally spanned across a spatial gap with cable endpoints fixed to the top edges of two glass beakers. The cable has been called a water bridge in close analogy to iron cables employed to build ordinary span bridges. A necessary condition for the construction of a water bridge is that a large electric field exists parallel to and located within the water cable. Presently, there is no accepted detailed theory which quantitatively explains the forces which hold up the bridge. Our purpose is to present such theory based on the Maxwell pressure tensor induced by the electric field albeit within the condensed matter dielectric fluid cable.

Raman spectroscopic investigations are carried out on ZnO nanoparticles for various photon energies. Intensities of E1-LO and E2 modes exhibit large changes as the excitation energy varied from 2.41 to 3.815 eV, signifying substantially large contribution of Frohlich interaction to the Raman polarizability as compared to deformation potential close to the resonance. Relative strength of these two mechanisms is estimated for the first time in nanoparticles and compared with those in the bulk., Comment: 13 pages. 3 figures Journal

We give an interpretation of the coefficients of the two variable refinement $D_{\Sh_n}(q,t)$ of the distance enumerator of the Shi hyperplane arrangement $\Sh_n$ in $n$ dimensions. This two variable refinement was defined by Stanley \cite{stan-rota} for the general $r$-extended Shi hyperplane arrangements. We give an interpretation when $r=1$. We define three natural three-dimensional partitions of the number $(n+1)^{n-1}$. The first arises from parking functions of length $n$, the second from special posets on $n$ vertices defined by Athanasiadis and the third from spanning trees on $n+1$ vertices. We call the three partitions as the parking partition, the tree-poset partition and the spanning-tree partition respectively. We show that one of the parts of the parking partition is identical to the number of edge-labelled trees with label set $\{1,2,...,n\}$ on $n+1$ unlabelled vertices. We prove that the parking partition majorises the tree-poset partition and conjecture that the spanning-tree partition also majorises the tree-poset partition., Comment: 11 pages, 8 figures

We give a Cayley type formula to count the number of spanning trees in the complete r-uniform hypergraph for all r >= 3. Similar to the bijection between spanning trees in complete graphs and Parking functions, we derive a bijection from spanning trees of the complete (r+1)-uniform hypergraph which arise from a fixed r-perfect matching and r-Parking functions. We observe a simple consequence of this bijection in terms of the number of regions of the extended Shi arrangement., Comment: 11 pages, 5 figures, corrected scores of errors, added a section on gen fns

The degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order. The polytope of degree partitions (respectively, degree sequences) is the convex hull of all degree partitions (respectively, degree sequences) of a fixed length. We think of the degree sequence polytope as the symmetrization of the degree partition polytope and the degree partition polytope as the asymmetric part of the degree sequence polytope. The degree sequence polytope is a well studied object with formulas (generating functions) known for its face numbers, volume, and number of lattice points. We study the degree partition polytope and determine its extreme points, edges, and facets. In particular, the degree partition polytope on n vertices has 2^{n-1} extreme points., Comment: 21 pages

The static Casimir effect concerns quantum electrodynamic induced Lamb shifts in the mode frequencies and thermal free energies of condensed matter systems. Sometimes, the condensed matter constitutes the boundaries of a vacuum region. The static frequency shift effects have been calculated in the one photon loop perturbation theory approximation. The dynamic Casimir effect concerns two photon radiation processes arising from time dependent frequency modulations again computed in the one photon loop approximation. Under certain conditions the one photon loop computation may become unstable and higher order terms must be invoked to achieve stable solutions. This stability calculation is discussed for a simple example dynamical Casimir effect system., Comment: LaTeX format, One Figure in *.eps format

Molecular quantum electrodynamics leads to photon frequency shifts and thus to changes in condensed matter free energies often called the Casimir effect. Strong quantum electrodynamic coupling between radiation and molecular motions can lead to an instability beyond which one or more photon oscillators undergo a displacement phase transition. The phase boundary of the transition can be located by a Casimir free energy instability., Comment: ReVTeX4 format 1 *.eps figure

The cross section for a gravitational wave antenna to absorb a graviton may be directly expressed in terms of the non-local viscous response function of the metallic crystal. Crystal viscosity is dominated by electronic processes which then also dominate the graviton absorption rate. To compute this rate from a microscopic Hamiltonian, one must include the full Coulomb interaction in the Maxwell electric field pressure and also allow for strongly non-adiabatic transitions in the electronic kinetic pressure. The view that the electrons and phonons constitute ideal gases with a weak electron phonon interaction is not sufficiently accurate for estimating the full strength of the electronic interaction with a gravitational wave., Comment: 7 pages LaTeX 1 figure afig1.eps

We consider light waves propagating clockwise and other light waves propagating counterclockwise around a closed path in a plane (theoretically with the help of stationary mirrors). The time difference between the two light propagating path orientations constitutes the Sagnac effect. The general relativistic expression for the Sagnac effect is discussed. It is shown that a gravitational wave incident to the light beams at an arbitrary angle will not induce a Sagnac effect so long as the wave length of the weak gravitational wave is long on the length scale of the closed light beam paths. The gravitational wave induced Sagnac effect is thereby null., Comment: LaTeX format 1 *.eps figure

Employing Maxwell's equations as the field theory of the photon, quantum mechanical operators for spin, chirality, helicity, velocity, momentum, energy and position are derived. The photon ``Zitterbewegung'' along helical paths is explored. The resulting non-commutative geometry of photon position and the quantum version of the Pythagorean theorem is discussed. The distance between two photons in a polarized beam of given helicity is shown to have a discrete spectrum. Such a spectrum should become manifest in measurements of two photon coincidence counts. The proposed experiment is briefly described., Comment: Latex, 13 pages, 3 figures

Electromagnetic methods recently proposed for detecting gravitational waves modify the Michelson phase shift analysis (historically employed for special relativity). We suggest that a frequency modulation analysis is more suited to general relativity. An incident photon in the presence of a very long wavelength gravitational wave will have a finite probability of being returned as a final photon with a frequency shift whose magnitude is equal to the gravitational wave frequency. The effect is due to the non-linear coupling between electromagnetic and gravitational waves. The frequency modulation is derived directly from the Maxwell-Einstein equations., Comment: 4 pages, 3 *.eps figures, RevTeX 4 format

The notion of ``radiating'' and ``non-radiating'' current sources in classical electrodynamics plays an important role in calculations of direct and inverse electromagnetic scattering problems. Such a decomposition of the current is central for the notion of localized non-radiating electromagnetic modes. A completely quantum electrodynamic view is explored in this work. Photon emission and absorption current sources are classified as being either radiating or non-radiating. This quantum classification corresponds, respectively and exactly, to the notion of ``real'' and ``virtual'' photon processes. Causal properties of both real and virtual electromagnetic fields are discussed., Comment: IOP LaTeX and one figure