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This work introduces a novel approach to achieving architecture-agnostic equivariance in deep learning, particularly addressing the limitations of traditional layerwise equivariant architectures and the inefficiencies of the existing architecture-agnostic methods. Building equivariant models using traditional methods requires designing equivariant versions of existing models and training them from scratch, a process that is both impractical and resource-intensive. Canonicalization has emerged as a promising alternative for inducing equivariance without altering model architecture, but it suffers from the need for highly expressive and expensive equivariant networks to learn canonical orientations accurately. We propose a new optimization-based method that employs any non-equivariant network for canonicalization. Our method uses contrastive learning to efficiently learn a canonical orientation and offers more flexibility for the choice of canonicalization network. We empirically demonstrate that this approach outperforms existing methods in achieving equivariance for large pretrained models and significantly speeds up the canonicalization process, making it up to 2 times faster., Comment: Accepted to EquiVision workshop, CVPR 2024. 8 pages, 2 figures, 2 tables

General relativity (GR) predicts the existence of black hole (BH). The rotating BH called as a Kerr Black hole and GR implies that there is an upper limit on the angular momentum per mass squared of black holes $\leq 1$, above which the event horizon of the Kerr BH is not exist. We find the radial equation for equatorial motion for Kerr BH in terms of the effective potential. We have shown the effective potential profile for different rotation parameter ($a$). We find the solution of the radial equation of the Kerr metric and found the expression of the angular momentum per unit mass squared, $\tilde a = \frac{a}{M}$. We showed the profile of $\tilde a$ as a function of $\frac{r}{M}$. The solution also leads the energy per unit rest mass ($e$) and we showed its behavior as a function of $\frac{r}{M}$. We enumerated the maximum values of radius of innermost stable circular orbit ($r_{ISCO}$) for $\tilde a=1$., Comment: 12 pages, 21 figures

In this study, we investigate the combination of indicators, including performance, behavioral engagement, and emotional engagement, to identify students experiencing difficulties. We analyzed data from two primary sources: digital traces extracted from th e Learning Management System (LMS) and images captured by students' webcams. The digital traces provided insights into students' interactions with the educational content, while the images were utilized to analyze their emotional expressions during learnin g activities. By utilizing real data collected from students at a French engineering school, recorded during the 2022 2023 academic year, we observed a correlation between positive emotional states and improved academic outcomes. These preliminary findings support the notion that emotions play a crucial role in differentiating between high achieving and low achieving students., Comment: 5 pages, 2 figures

Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component of prevalent deep neural network architectures to achieve chosen equivariance is a difficult problem and can result in a computationally expensive network during both training and inference. A recently proposed alternative towards equivariance that removes the architectural constraints is to use a simple canonicalization network that transforms the input to a canonical form before feeding it to an unconstrained prediction network. We show here that this approach can effectively be used to make a large pretrained network equivariant. However, we observe that the produced canonical orientations can be misaligned with those of the training distribution, hindering performance. Using dataset-dependent priors to inform the canonicalization function, we are able to make large pretrained models equivariant while maintaining their performance. This significantly improves the robustness of these models to deterministic transformations of the data, such as rotations. We believe this equivariant adaptation of large pretrained models can help their domain-specific applications with known symmetry priors., Comment: 17 pages, 6 figures. Accepted to NeurIPS 2023

This paper presents an investigation into machine learning techniques for violence detection in videos and their adaptation to a federated learning context. The study includes experiments with spatio-temporal features extracted from benchmark video datasets, comparison of different methods, and proposal of a modified version of the "Flow-Gated" architecture called "Diff-Gated." Additionally, various machine learning techniques, including super-convergence and transfer learning, are explored, and a method for adapting centralized datasets to a federated learning context is developed. The research achieves better accuracy results compared to state-of-the-art models by training the best violence detection model in a federated learning context., Comment: 8 pages, 2 figures, FL-IJCAI'23

The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could advance Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging. Inaccuracies in model estimates can compound, resulting in increased errors over long horizons. We approach this problem from the lens of Koopman theory, where the nonlinear dynamics of the environment can be linearized in a high-dimensional latent space. This allows us to efficiently parallelize the sequential problem of long-range prediction using convolution while accounting for the agent's action at every time step. Our approach also enables stability analysis and better control over gradients through time. Taken together, these advantages result in significant improvement over the existing approaches, both in the efficiency and the accuracy of modeling dynamics over extended horizons. We also show that this model can be easily incorporated into dynamics modeling for model-based planning and model-free RL and report promising experimental results., Comment: Accepted to ICLR 2024 and EWRL 2023

Inverse design of short single-stranded RNA and DNA sequences (aptamers) is the task of finding sequences that satisfy a set of desired criteria. Relevant criteria may be, for example, the presence of specific folding motifs, binding to molecular ligands, sensing properties, etc. Most practical approaches to aptamer design identify a small set of promising candidate sequences using high-throughput experiments (e.g. SELEX), and then optimize performance by introducing only minor modifications to the empirically found candidates. Sequences that possess the desired properties but differ drastically in chemical composition will add diversity to the search space and facilitate the discovery of useful nucleic acid aptamers. Systematic diversification protocols are needed. Here we propose to use an unsupervised machine learning model known as the Potts model to discover new, useful sequences with controllable sequence diversity. We start by training a Potts model using the maximum entropy principle on a small set of empirically identified sequences unified by a common feature. To generate new candidate sequences with a controllable degree of diversity, we take advantage of the model's spectral feature: an energy bandgap separating sequences that are similar to the training set from those that are distinct. By controlling the Potts energy range that is sampled, we generate sequences that are distinct from the training set yet still likely to have the encoded features. To demonstrate performance, we apply our approach to design diverse pools of sequences with specified secondary structure motifs in 30-mer RNA and DNA aptamers.

A new optical technique based on light-matter interaction is devised in-house to detect thermo-acoustic disturbances generated after ignition and during propagation of a premixed flame front in a half open channel. The technique involves passing a polarized laser light through a medium whose density or refractive index varies due to the passage of acoustic waves and/or flame front and then capturing the leaked depolarised light through an analyser by a photo-detector. The technique is applied to combustor involving premixed flame propagation and tulip inversion. The thermo-acoustic signals and the flame front are distinguished by comparing the oscilloscope signal with high speed photography of the flow-field. Acoustic waves are found to intercept the flame propagation at various axial locations and time instants.

A novel third order nonlinear evolution equation governing the dynamics of high frequency electrostatic drift waves has been derived in the framework of a plasma fluid model in an inhomogeneous magnetized plasma. The linear dispersion relation arising out of the fluid equations has been studied for the conventional low frequency and high frequency electrostatic drift waves. This equation is then decomposed into two second order equations as the order of the equation becomes reduced after this kind of decomposition under certain conditions. The detailed analysis of fixed points as well as bifurcations of the phase portraits have been performed using the theory of planar dynamical systems. Then some exact as well as approximate travelling wave solutions of this reduced nonlinear equation for the high frequency electrostatic drift waves are derived. As the other second order reduced equation is linear in nature, its exact oscillatory and exponential solutions are derived. The intersection of the solutions of these two reduced second order equations provides the solutions of the original third order nonlinear evolution equation; it is verified that the solutions of the reduced nonlinear second order equation are subsets of the oscillatory solution of the reduced linear second order equation in most cases whereas the intersection is different if the exponential solution of the reduced linear second order equation is considered. So the solutions of the reduced second order nonlinear equation can directly represent the solutions of the original third order nonlinear equation representing the dynamics of the nonlinear high frequency electrostatic drift waves if the oscillatory solution of the reduced linear equation is considered., Comment: 28 pages and 14 figures

We present the system description for our submission towards the Key Point Analysis Shared Task at ArgMining 2021. Track 1 of the shared task requires participants to develop methods to predict the match score between each pair of arguments and keypoints, provided they belong to the same topic under the same stance. We leveraged existing state of the art pre-trained language models along with incorporating additional data and features extracted from the inputs (topics, key points, and arguments) to improve performance. We were able to achieve mAP strict and mAP relaxed score of 0.872 and 0.966 respectively in the evaluation phase, securing 5th place on the leaderboard. In the post evaluation phase, we achieved a mAP strict and mAP relaxed score of 0.921 and 0.982 respectively. All the codes to generate reproducible results on our models are available on Github.

The cells and their spatial patterns in the tumor microenvironment (TME) play a key role in tumor evolution, and yet the latter remains an understudied topic in computational pathology. This study, to the best of our knowledge, is among the first to hybridize local and global graph methods to profile orchestration and interaction of cellular components. To address the challenge in hematolymphoid cancers, where the cell classes in TME may be unclear, we first implemented cell-level unsupervised learning and identified two new cell subtypes. Local cell graphs or supercells were built for each image by considering the individual cell's geospatial location and classes. Then, we applied supercell level clustering and identified two new cell communities. In the end, we built global graphs to abstract spatial interaction patterns and extract features for disease diagnosis. We evaluate the proposed algorithm on H&E slides of 60 hematolymphoid neoplasms and further compared it with three cell level graph-based algorithms, including the global cell graph, cluster cell graph, and FLocK. The proposed algorithm achieved a mean diagnosis accuracy of 0.703 with the repeated 5-fold cross-validation scheme. In conclusion, our algorithm shows superior performance over the existing methods and can be potentially applied to other cancer types., Comment: Accepted by MICCAI2021

The excitations of nonlinear magnetosonic waves in presence of charged space debris in the low Earth orbital plasma region is investigated taking into account effects of electron inertia in the framework of classical magnetohydrodynamics, which is also referred to as inertial magnetohydrodynamics. Magnetosonic waves are found to be governed by a forced Kadomtsev-Petviashvili equation with the forcing term representing effects of space debris particles. The dynamical behaviors of both slow and fast magnetosonic solitary waves is explored in detail. Exact accelerated magnetosonic lump solutions are shown to be stable for the entire region in parameter space of slow waves and a large region in parameter space of fast waves. In a similar way, magnetosonic curved solitary waves become stable for a small region in parameter space of fast waves. These exact solutions with special properties are derived for specific choices of debris functions. These novel results can have potential applications in scientific and technological aspects of space debris detection and mitigation., Comment: 13 pages and 9 figures

The excitations of nonlinear magnetosonic lump waves induced by orbiting charged space debris objects in the Low Earth Orbital (LEO) plasma region are investigated in presence of the ambient magnetic field. These nonlinear waves are found to be governed by the forced Kadomtsev-Petviashvili (KP) type model equation, where the forcing term signifies the source current generated by different possible motions of charged space debris particles in the LEO plasma region. Different analytic lump wave solutions that are stable for both slow and fast magnetosonic waves in presence of charged space debris particles are found for the first time. The dynamics of exact pinned accelerated lump waves is explored in detail. Approximate lump wave solutions with time-dependent amplitudes and velocities are analyzed through perturbation methods for different types of localized space debris functions; yielding approximate pinned accelerated lump wave solutions. These new results may pave new direction in this field of research., Comment: 21 Pages and 10 Figures

We consider a low temperature plasma environment in the Low Earth Orbital (LEO) region in presence of charged space debris particles. The dynamics of (2+1) dimensional nonlinear dust ion acoustic waves with weak transverse perturbation, generated in the system is found to be governed by a forced Kadomtsev-Petviashvili (KP) equation, where the forcing term depends on charged space debris function. The bending phenomena of some exact dust ion acoustic solitary wave solutions in x-t and x-y planes are shown; that are resulted from consideration of different types of possible localized debris functions. A family of exact pinned accelerated solitary wave solutions has been obtained where the velocity changes over time but the amplitude remains constant. The shape of debris function also changes during its propagation. Also, a special exact solitary wave solution has been derived for the dust ion acoustic wave; that gets curved in spatial dimensions with the curvature depending upon nature of forcing debris function. Such intricate solitary wave solutions may be useful in modelling real experimental data., Comment: 15 pages, 8 figures

Genetic circuits are designed to implement certain logic in living cells, keeping burden on the host cell minimal. However, manipulating the genome often will have a significant impact for various reasons (usage of the cell machinery to express new genes, toxicity of genes, interactions with native genes, etc.). In this work we utilize Koopman operator theory to construct data-driven models of transcriptomic-level dynamics from noisy and temporally sparse RNAseq measurements. We show how Koopman models can be used to quantify impact on genetic circuits. We consider an experimental example, using high-throughput RNAseq measurements collected from wild-type E. coli, single gate components transformed in E. coli, and a NAND circuit composed from individual gates in E. coli, to explore how Koopman subspace functions encode increasing circuit interference on E. coli chassis dynamics. The algorithm provides a novel method for quantifying the impact of synthetic biological circuits on host-chassis dynamics., Comment: 4 pages Accepted in 2019 IEEE Biomedical Circuits and Systems Conference

We have analyzed the prospects of observing the lightest CP-even neutral Higgs boson ($h_1$) via decays into $b \bar b$ pairs in the neutral and charged current production processes $e^- q \to e^- h_1 q$ and $e^- q\to \nu_e h_1 q'$, respectively, at the planneded large Hadron electron Collider (LHeC), with an $e^-$ beam energy of 60 GeV and a $p$ beam energy of 7 TeV. We also focus on observing a relatively light charged Higgs boson ($h^{-}$) via its production mode $e^- b \to \nu_e h^{-} b$ followed by the decays $h^{-} \to s \bar c + s \bar u$ at the upcoming Future Circular Collider in hadron-electron mode (FCC-eh) with $\sqrt s \approx 3.5$ TeV. We have performed our analysis in the framework of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) wherein the intermediate Higgs boson ($h_2$) is Standard Model (SM)-like. We have considered constraints from Dark Matter (DM), superparticle and the Higgs boson data. In both analyses, we have carried out signal and background computations with selections optimized to the model at hand and found that in both cases it is possible to get large significances for low mass Higgs bosons., Comment: 5 pages, 6 figures. Proceedings from PIC2018: XXXVIII International Symposium on Physics in Collision, Bogot\'a, Colombia, 2018. Based on arXiv:1612.07241 and arXiv:806.08361

We study the potential of the LHC accelerator, and a future 33 TeV proton collider, to observe the production of a light top squark pair in association with the lightest Higgs boson (${\tilde t}_1 {\tilde t}_1 h_1$), as predicted by the Next-to-Minimal Supersymmetric Standard Model (NMSSM). We scan randomly about ten million points of the NMSSM parameter space, allowing all possible decays of the lightest top squark and lightest Higgs boson, with no assumptions about their decay rates, except for known physical constraints such as perturbative bounds, Dark matter relic density consistent with recent Planck experiment measurements, Higgs mass bounds on the next to lightest Higgs boson, $h_2$, assuming it is consistent with LHC measurements for the Standard Model Higgs boson, LEP bounds for the chargino mass and Z invisible width, experimental bounds on B meson rare decays and some LHC experimental bounds on SUSY particle spectra different to the particles involved in our study. We find that for low mass top-squark, the dominating decay mode is ${\tilde t}_1 \rightarrow b \tilde{\chi}_1^{\pm}$ with $\tilde{\chi}_1^{\pm} \rightarrow W^{\pm} \tilde{\chi}_1^0 $. We use three bench mark points with the highest cross sections, which naturally fall within the compressed spectra of the top squark, and make a phenomenological analysis to determine the optimal event selection that maximizes the signal significance over backgrounds. We focus on the leptonic decays of both $W$'s and the decay of lightest Higgs boson into b-quarks ($h_1 \rightarrow b \bar b$). Our results show that the high luminosity LHC will have limitations to observe the studied signal and only a proton collider with higher energy will be able to observe the SUSY scenario studied with more than three standard deviations over background., Comment: 26 pages, 14 figures, Few figures updated and new references added

We analyze the prospects of observing the light CP-even neutral Higgs bosons ($h_1$) in their decays into $b \bar b$ quarks, in the neutral and charged current production processes $e h_1 q$ and $\nu h_1 q$ at the upcoming LHeC, with $\sqrt s \approx 1.296$ TeV. Assuming that the intermediate Higgs boson ($h_2$) is Standard Model (SM)-like, we study the Higgs production within the framework of NMSSM. We consider the constraints from Dark-matter, Sparticle masses, and the Higgs boson data. The signal in our analysis can be classified as three jets, with electron (missing energy)coming from the neutral (charged) current interaction. We demand that the number of b-tagged jets in the central rapidity region be greater or equal to two. The remaining jet is tagged in the forward regions. With this forward jet and two $b$-tagged jets in the central region, we reconstructed three jets invariant masses. Applying some lower limits on these invariant masses turns out to be an essential criterion to enhance the signal--to--background rates, with slightly different sets of kinematical selections in the two different channels. We consider almost all reducible and irreducible SM background processes. We find that the non-SM like Higgs boson, $h_1$, would be accessible in some of the NMSSM benchmark points, at approximately 0.4$\sigma$ (2.5$\sigma$) level in the $e$+3j channel up to Higgs boson masses of 75 GeV and in the $E\!\!\!\!/_T$+3j channel could be discovered with 1.7$\sigma$ (2.4$\sigma$) level up to Higgs boson masses of 88 GeV with 100 fb$^{-1}$ of data in a simple cut-based (with optimization) selection. With ten times more data accumulation at the end of the LHeC run and using optimization, one can have 5$\sigma$ discovery in the electron (missing energy) channel up to 85 (more than 90) GeV., Comment: 38 pages, 27 figures, version to be appeared in Phys.Rev.D

Non-universal gaugino mass models can naturally account for the dark matter relic density via the bulk annihilation process with relatively light bino LSP and right sleptons in the mass range of ~ 100 GeV, while accommodating the observed Higgs boson mass of ~ 125 GeV with TeV scale squark/gluino masses. A class of these models can also account for the observed muon g-2 anomaly via SUSY loops with wino and left sleptons in the mass range of 400 -- 700 GeV. These models can be tested at LHC via electroweak production of charged and neutral wino pair, leading to robust trilepton and same sign dilepton signals. We investigate these signals along with the standard model background for both 8 and 13 TeV LHC runs., Comment: 14 pages, version to be published in PRD

We propose a dynamic slicing algorithm to compute the slice of concurrent aspect-oriented programs. We use a dependence based intermediate program representation called Concurrent Aspect-oriented System Dependence Graph (CASDG) to represent a concurrent aspect-oriented program. The CASDG of an aspect-oriented program consists of a system dependence graph (SDG) for the non-aspect code, a group of dependence graphs for aspect code and some additional dependence edges used to connect the system dependence graph for the non-aspect code to dependence graph for aspect code. The proposed dynamic slicing al-gorithm is an extended version of NMDS algorithm for concurrent object-oriented programs, which is based on marking and unmarking of the executed nodes in CASDG appropriately during run-time., Comment: 20 pages. arXiv admin note: text overlap with arXiv:1403.0100

We propose a dynamic slicing algorithm to compute the slices of aspect-oriented programs. We use a dependence based intermediate program representation called Aspect System Dependence Graph (AOSG) to represent aspect-oriented programs. Then, we propose the dynamic slicing algorithm for AOPs, which is an extended version of EMDS algorithm for object-oriented programs. Our algorithm is based on marking and unmarking of the edges of AOSG appropriately during runtime., Comment: 7 Pages

We consider the process $p p \to t {\bar t} H$. This process can give rise to many signatures of the Higgs boson. The signatures can have electrons, muons and jets. We consider the signatures that have two electrons/muons and jets. Tagging of a tau jet and a bottom jet can help reduce the backgrounds significantly. In particular, we examine the usefulness of the signatures "isolated 2 electrons/muons + a bottom jet + a tau jet", "isolated 2 electrons/muons + 2 tau jets", "isolated 2 electrons/muons + 2 bottom jets + a tau jet", and "isolated 2 electrons/muons + a bottom jet + 2 tau jets". We find that signatures with two tau jets are useful. The signatures with one tau jet are also useful, if we restrict to same-sign electrons/muons. These requirements reduce the backgrounds due the process with Z-bosons + jets and the production of a pair of top quarks. We show that these signatures may be visible in the run II of the Large Hadron Collider., Comment: 15 pages, 1 figure, added discussions, added references, conclusion unchanged

We consider the possible production of the Higgs Boson in association with a top-quark pair and its subsequent decay into a tau-lepton pair or a W-boson pair. This process can give rise to many signatures of the Higgs boson. These signatures can have electrons, muons, tau jets, bottom jets and/or light flavour jets. We analyze the viability of some of these signatures. We will look at those signatures where the background is minimal. In particular, we explore the viability of the signatures "isolated 4 electron/muon" and "isolated 3 electron/muon + a jet" The jet can be due to a light flavour quark/gluon, a bottom quark, or a tau lepton. Of all these signatures, we find that "isolated 3 electron/muon + a tau jet", with an extra bottom jet, can be an excellent signature of this mode of the Higgs boson production. We show that this signature may be visible within a year, once the Large Hadron Collider (LHC) restarts. Some of the other signatures would also be observable after the LHC accumulates sufficient luminosity., Comment: 11 pages, 1 Figure

We analyze the prospect for observing the intermediate neutral Higgs boson ($h_2$) in its decay to two lighter Higgs bosons ($h_1$) at the presently operating hadron colliders in the framework of the CP violating MSSM using the PYTHIA event generator. We consider the lepton+ 4-jets+ $\met$ channel from associate $W h_2$ production, with $W h_2 \ra W h_1 h_1 \ra \ell \nu_\ell b \bar b b\bar b$. We require two, three or four tagged $b$-jets. We explicitly consider all relevant Standard Model backgrounds, treating $c$-jets separately from light flavor and gluon jets and allowing for mistagging. We find that it is very hard to observe this signature at the Tevatron, even with 20 fb$^{-1}$ of data, in the LEP--allowed region of parameter space due to the small signal efficiency, even though the background is manageable. At the LHC, a priori huge SM backgrounds can be suppressed by applying judiciously chosen kinematical selections. After all cuts, we are left with a signal cross section of around 0.5 fb, and a signal to background ratio between 1.2 and 2.9. According to our analysis this Higgs signal should be viable at the LHC in the vicinity of present LEP exclusion once 20 to 50 fb$^{-1}$ of data have been accumulated at $\sqrt{s}=14$ TeV., Comment: 27 pages, 12 figures

We analyze the prospect for observing the intermediate neutral Higgs boson ($h_2$) in its decay to two lighter Higgs bosons ($h_1$) at the presently operating hadron colliders in the framework of the CP violating MSSM using the PYTHIA event generator. We consider the lepton+ 4-jets+ $\met$ channel from associate $W h_2$ production, with $W h_2 \ra W h_1 h_1 \ra \ell \nu_\ell b \bar b b\bar b$. We require two or three tagged $b$-jets. We explicitly consider all relevant Standard Model backgrounds, treating $c$-jets separately from light flavor and gluon jets and allowing for mistagging. We find that it is very hard to observe this signature at the Tevatron, even with 20 fb$^{-1}$ of data, in the LEP--allowed region of parameter space due to the small signal efficiency. At the LHC, a priori huge SM backgrounds can be suppressed by applying judiciously chosen kinematical selections. After all cuts, we are left with a signal cross section of around 0.5 fb, and a signal to background ratio between 1.2 and 2.9. According to our analysis this Higgs signal should be viable at the LHC in the vicinity of present LEP exclusion once 20 to 50 fb$^{-1}$ of data have been accumulated at $\sqrt{s}=14$ TeV., Comment: 6 pages, 2 figures, talk presented at PASCOS 2010(Valencia) and SUSY 10(Bonn)

We consider the minimal supergravity model (mSUGRA) with one additional R-parity violating operator at the GUT scale. The superparticles mass spectra at the weak scale are generally altered due to the presence of the R-parity violating coupling in the renormalization group equations. We show that a lepton number violating coupling at the GUT scale can lead to a sneutrino as the lightest supersymmetric particle (LSP) in a large region of parameter space consistent with the muon anomalous magnetic moment and other precision measurements. We also give characteristic collider signatures at the LHC., Comment: 3 pages, 3 figures, to appear in the proceedings of SUSY08, Seoul, Korea

We analyze the prospect for observing the intermediate neutral Higgs ($h_2$) boson in its decay to two lighter Higgs bosons ($h_1$) at the Tevatron in the framework of the CP violating MSSM using the PYTHIA event generator. We consider the lepton+ 4-jets+ $\met$ channel from $p \bar p \ra W h_2 \ra W h_1 h_1 \ra l \nu_l b \bar b b\bar b$, with two or three tagged $b$ jets. We found that it is very hard to observe this signature in the LEP-allowed region of parameter space, due to the small signal efficiency., Comment: 3 pages, 3 figures, to appear in the proceedings of SUSY08, Seoul, Korea

The estimation of the backgrounds for gluino signals in focus point supersymmetry is extended by including the backgrounds from the production of four third generation quarks in the analysis. We find that these backgrounds are negligible if one uses the strong selection criteria proposed in the literature (including this analysis) for heavy gluino searches. Softer selection criteria often recommended for lighter gluino searches yield backgrounds which are small but numerically significant. We have also repeated the more conventional background calculations and compared our results with the other groups. We find that the size of the total residual background estimated by different groups using different event generators and hard kinematical cuts agree approximately. In view of the theoretical uncertainties in the leading order signal and background cross sections mainly due to the choice of the QCD scale, the gluino mass reach at the LHC cannot be pinpointed. However, requiring a signal with $\rm\geq 3$ tagged b-jets (instead of the standard choice of $\rm\geq 2$) it is shown that gluino masses close to 2 TeV can be probed at the LHC for a range of reasonable choices of the QCD scale for an integrated luminosity of 300 fb$^{-1}$., Comment: 17 pages, 4 figures, minor typos correction

We reinvestigated the parameter space allowing a large BR of the 4-body decay of the lighter top-squark ($\lstop$) accessible at Tevatron Run-II by imposing the lighter CP-even Higgs boson mass ($\mlhiggs$) bound from LEP. Important constraints were obtained in mSUGRA as well as in the unconstrained supersymmetric models. Our results show that the prospect of searching the lighter top-squark via the 4-body decay mode, in particular the $\ell + n-jets + \met$ signal, is not promising in mSUGRA due to the above bound on $\mlhiggs$. The existing bounds on $\mlstop$ from Tevatron Run-I and LEP assuming 100% BR of the loop decay of $\lstop$ are, therefore, valid to a good approximation. We also find that large BRs of the above 4-body decay are allowed in the unconstrained model over significant regions of parameter spaces and the possibility that this decay mode is the main discovery channel at Tevatron Run-II is open. We have briefly reviewed the theoretical uncertainties in the calculation of $\mlhiggs$ and their consequences for the constraints obtained by us. We have commented upon, with illustrative examples, how the above parameter space is affected if future experiments push the Higgs boson mass bound upward., Comment: 24 pages, 14 figures, added comments in sec.1, added 2 figures and comments in sec.2.1, conclusion and references updated

In a R-parity violating (RPV) model of neutrino mass with three bilinear couplings $\mu_i$ and three trilinear couplings $\lambda'_{i33}$, where $i$ is the lepton index, we find six generic scenarios each with a distinctive pattern of the trilinear couplings consistent with the oscillation data. These patterns may be reflected in direct RPV decays of the lighter top squark or in the RPV decays of the lightest superparticle, assumed to be the lightest neutralino. Typical signal sizes at the Tevatron RUN II and the LHC have been estimated and the results turn out to be encouraging., Comment: 20 pages, 4 figures, LaTex,typos corrected and reference added for section 2, a paragraph has been added in the conclusion part

This is a summary of the projects undertaken by the Working Group I on High Energy Collider Physics at the Eighth Workshop on High Energy Physics Phenomenology (WHEPP8) held at the Indian Institute of Technology, Mumbai, January 5-16, 2004. The topics covered are (i) Higgs searches (ii) supersymmetry searches (iii) extra dimensions and (iv) linear collider., Comment: summary of Working Group I at the Eighth Workshop on High Energy Physics Phenomenology (WHEPP8), I.I.T., Mumbai, January 5-16, 2004

Analyzing the $\ell +n$-$jets+ \met$ (where $n \ge 2 $), data from Run-I of the Tevatron using the Bayesian technique, we obtain model independent limits on the product $\br(\lstop\ra be^{+}\nu_e \lspone) \times \br(\lstop^{*}\ra \bar{b}q\bar{q^{\prime}}\lspone)$ for different values of the lighter top squark($\lstop$) mass and the lightest supersymmetric particle($\lspone$) mass. The SUSY signals have been simulated by interfacing the 4-body decay of $\lstop$ at the parton level with the event generator PYTHIA. These limits have been translated into exclusion plots in the $\mlstop$-$\mlspone$ plane, which also turn out to be fairly model independent for fixed values of the BR of the competing loop decay mode $\lstop\ra c \lspone$. Assuming the loop decay BR to be negligible and using the leading order cross section for $\lstoplstop$ pair production, we obtain conservatively $\mlstop \ge $77.0 (74.5) GeV for $\mlspone$=5(15) GeV, while for $\br(\lstop\ra c \lspone)$=20%, the corresponding limits are $\mlstop \ge $68.0 (65.0) GeV. Using the larger next to leading order cross-section stronger limits are obtained. For example, if $\br(\lstop\ra c \lspone)$=20%, $\mlstop \ge $73.0 (72.7) GeV for $\mlspone$=5(15) GeV. Our limits nicely complement the ALEPH bounds which get weaker for low $\mlspone$., Comment: 11 pages, 5 figures, few comments added

We have estimated the limiting branching ratio of the R-parity violating (RPV) decay of the lighter top squark, $\tilde t_1 \ar l^+ d$ ($l=e$ or $\mu $ and d is a down type quark of any flavor), as a function of top squark mass($\MST$) for an observable signal in the di-lepton plus di-jet channel at the Tevatron RUN-II experiment with 2 fb$^{-1}$ luminosity. Our simulations indicate that the lepton number violating nature of the underlying decay dynamics can be confirmed via the reconstruction of $\MST$. The above decay is interesting in the context of RPV models of neutrino mass where the RPV couplings ($\lambda'_{i3j}$) driving the above decay are constrained to be small ($\lsim 10^{-3} - 10^{-4} $). If $\tilde t_1$ is the next lightest super particle - a theoretically well motivated scenario - then the RPV decay can naturally compete with the R-parity conserving (RPC) modes which also have suppressed widths. The model independent limiting BR can delineate the parameter space in specific supersymmetric models, where the dominating RPV decay is observable and predict the minimum magnitude of the RPV coupling that will be sensitive to Run-II data. We have found it to be in the same ballpark value required by models of neutrino mass, for a wide range of $\MST$. A comprehensive future strategy for linking top squark decays with models of neutrino mass is sketched., Comment: 28 pages, 14 Figures

We investigate the prospect of stop squark search at Tevatron RUN-II in mSUGRA motivated as well as unconstrained supersymmetric models, when the lighter stop squark turns out to be the next lightest supersymmetric particle (NLSP). In this case the decay into a 4-body final state consisting of a b quark, the lightest neutralino and two light fermions may compete with the much publicized loop induced two body decay into a charm quark and the lightest neutralino. We systematically study the parameter space in mSUGRA where the lighter stop squark turns out to be the NLSP and calculate the branching ratios of the competing channels in both models. Our results show that the four body decay may indeed be the main discovery channel particularly in the low tan $\beta$ scenarios. We discuss the detectability of stop squark pairs in the 4-body decay channel leading to one lepton with 2 or more jets accompanied by a large amount of missing energy. We also studied the corresponding background processes and the kinematic cuts required to suppress them using parton level Monte Carlo simulations. We have commented upon with illustrative examples, the required revision of the existing mass limits of the stop NLSP assumed to decay solely into the loop induced 2-body channel in the presence of the competing 4-body decay., Comment: 16 pages, latex, 6 figures