The last decade has seen considerable advances in our understanding of the genome, and computational methods have played a very crucial role in these developments. Decoding the human genome posed a significant computational challenge and is undoubtedly one of our major accomplishments; today, research is intently focused on understanding the sequences at an unprecedented level of detail. This process is continuously generating a steady stream of interesting computational problems. In this dissertation, we concentrate on several such problems arising from the need to understand the structural and functional organization of the nuclear components from microscopic images.
The first problem we study is related to extracting the same or similar 'foreground' from a set of image slices. The set of 2D slices correspond to images of the 3D chromosome acquired at different focal planes of the fluorescent microscope. But since the resolution in-plane (in the 2D slice) is higher than the resolution along the stack, a standard three dimensional segmentation is rather problematic. Our view of this problem is to perform figure-ground segmentation in the 2D planes individually with the additional condition that the foregrounds must be consistent w.r.t. each other. We design new based algorithms for this paired segmentation problem formulating it as a Markov Random Field (MRF) type energy function and report on encouraging results on a variety of images.
The second problem we tackle is the Generalized Median Graph problem motivated from the requirement of building topological maps of chromosome organization in the nucleus. The problem belongs to a class of prototype building problems where the input class is a set of graphs; in other words, we want to build a 'model graph' for a set of graphs. Our main result is a polynomial time algorithm for this problem which yields near-optimal solutions in practice. We show that using our LP based algorithm, even in the worst case, a solution within a factor of two of the optimal solution can be obtained if the distances between the graphs are known correctly. We propose an additional algorithm based on a bi-level framework to obtain solutions arbitrarily close to the optimal but in non-polynomial time.
The third problem we address is an important partial matching problem of geometric objects. The input is in the form of sets of under-sampled slices (e.g., 2D contours) of one (or more) unknown 3D objects (e.g., 3D chromatin surfaces), possibly generated by slicing planes of arbitrary orientations, the question we are interested in is whether it is 'possible' that two under-sampled sets have been taken from the same object. Since the three dimensional structure of objects of interest (e.g., chromosomes) often cannot be inferred precisely in fluorescence microscopy because of poor resolution in the third dimension, such techniques are important to establish correspondence between structures in a sequence of time-lapse images. We present efficient algorithms for addressing this question.
Next, we propose new approaches for analyzing time-lapse microscopic nuclear images. Our techniques address the problem of limited spatial and temporal resolution capacities of current microscopic imaging techniques which allow acquisition of images only in time-lase mode (which leads to significant frame-to-frame information loss). We present a suite of geometric approaches for solving the problem. Our techniques provide a comprehensive solution to (1) raw image simplification (2) segmentation and (3) effective recovery of complicated motion and deformation as well as the change of intensity surfaces from pairs of images in a microscopic image sequence. These techniques are also readily applicable to other types of images for reconstructing motion and intensity surfaces of deform able objects.
Finally, we propose a set of novel techniques to determine, analyze, and interpret the mobility patterns of functional sites (replication and transcription) in the nucleus. This is motivated from recent studies that have shown a link between movement of the sites and the actively expressing components of DNA. Our algorithms provide the tools to interpret the seemingly stochastic motion patterns of the functional sites within the nucleus in terms of a set of tractable 'patterns' which can then be analyzed to understand their biological significance.
We study flavor changing neutral current decays of $B$ and $K$ mesons in the dark $U(1)_D$ model, with the dark photon/dark $Z$ mass between 10 MeV and 2 GeV. Although the model provides an improved fit (compared to the standard model) to the differential decay distributions of $B \to K^{(*)} \ell^+ \ell^-$, with $\ell= μ, e$, and $B_s \to ϕμ^+ μ^-$, the allowed parameter space is ruled out by measurements of atomic parity violation, $K^+ \to μ^+ + invisible$ decay, and $B_s - \overline{B}_s$ mixing, among others. To evade constraints from low energy data, we extend the model to allow for (1) additional invisible $Z_D$ decay, (2) a direct vector coupling of $Z_D$ to muons, and (3) a direct coupling of $Z_D$ to both muons and electrons, with the electron coupling fine-tuned to cancel the $Z_D$ coupling to electrons via mixing. We find that only the latter case survives all constraints.
In this talk I discuss about some anomalous results in flavour physics and try to correlate them with the Inert Higgs doublet dark matter model. This is achieved by considering an extension of the Inert Higgs doublet model with $SU(2)_L$ singlet vector like fermions. Flavour data in $b \to s \ell \ell$ decay observables (like $R(K)$, $R(K^*)$) and muon $(g-2)$ puts stringent bounds on the model parameters. The model can simultaneously satisfy relevant constraints in the dark matter sector and also abide by the bounds given by the ongoing direct detection experiments. I also discuss the discovery possibilities of such exotics in the future high luminosity (HL) runs of the LHC.
A bstract In this work, we explore the effect of neutrino nonstandard interactions (NSI) involving the charm quark at SND@LHC. Using an effective description of new physics in terms of four-fermion operators involving a charm quark, we constrain the Wilson coefficients of the effective interaction from two and three-body charmed meson decays. In our fit, we include charmed meson decays not only to pseudoscalar final states but also to vector final states and include decays to the η and η ′ final states. We also consider constraints from charmed baryon decays. We then study the effect of new physics in neutrino scattering processes, involving charm production at SND@LHC, for various benchmark new physics couplings obtained from the low energy fits. Finally, we also study the effects of lepton universality violation (LUV) assuming that the new physics coupling is not lepton universal.
Microglia are the immune cell in the central nervous system (CNS) and exist in a surveillant state characterized by a ramified form in the healthy brain. In response to brain injury or disease including neurodegenerative diseases, they become activated and change their morphology. Due to known correlation between this activation and neuroinflammation, there is great interest in improved approaches for studying microglial activation in the context of CNS disease mechanisms. One classic approach has utilized Microglia's morphology as one of the key indicators of its activation and correlated with its functional state. More recently microglial activation has been shown to have intrinsic NADH metabolic signatures that are detectable via fluorescence lifetime imaging (FLIM). Despite the promise of morphology and metabolism as key fingerprints of microglial function, they has not been analyzed together due to lack of an appropriate computational framework. Here we present a deep neural network to study the effect of both morphology and FLIM metabolic signatures toward identifying its activation status. Our model is tested on 1, 000+ cells (ground truth generated using LPS treatment) and provides a state-of-the-art framework to identify microglial activation and its role in neurodegenerative diseases.
Our primary interest is in generalizing the problem of Cosegmentation to a large group of images, that is, concurrent segmentation of common foreground region(s) from multiple images. We further wish for our algorithm to offer scale invariance (foregrounds may have arbitrary sizes in different images) and the running time to increase (no more than) near linearly in the number of images in the set. What makes this setting particularly challenging is that even if we ignore the scale invariance desiderata, the Cosegmentation problem, as formalized in many recent papers (except), is already hard to solve optimally in the two image case. A straightforward extension of such models to multiple images leads to loose relaxations; and unless we impose a distributional assumption on the appearance model, existing mechanisms for image-pair-wise measurement of foreground appearance variations lead to significantly large problem sizes (even for moderate number of images). This paper presents a surprisingly easy to implement algorithm which performs well, and satisfies all requirements listed above (scale invariance, low computational requirements, and viability for the multiple image setting). We present qualitative and technical analysis of the properties of this framework.
We consider the ensemble clustering problem where the task is to 'aggregate' multiple clustering solutions into a single consolidated clustering that maximizes the shared information among given clustering solutions. We obtain several new results for this problem. First, we note that the notion of agreement under such circumstances can be better captured using an agreement measure based on a 2D string encoding rather than voting strategy based methods proposed in literature. Using this generalization, we first derive a nonlinear optimization model to maximize the new agreement measure. We then show that our optimization problem can be transformed into a strict 0-1 Semidefinite Program (SDP) via novel convexification techniques which can subsequently be relaxed to a polynomial time solvable SDP. Our experiments indicate improvements not only in terms of the proposed agreement measure but also the existing agreement measures based on voting strategies. We discuss evaluations on clustering and image segmentation databases.
Belle II has reported the first evidence for $B^+ \to K^+ν\barν$ with a branching ratio $2.8 σ$ higher than the standard model expectation. We explain this, and the MiniBooNE and muon anomalous magnetic moment anomalies in a model with a dark scalar that couples to a slightly heavier sterile Dirac neutrino and that communicates with the visible sector via a Higgs portal. We make predictions for rare kaon and other $B$ meson decays.
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