An In-Place Sorting with O(n log n) Comparisons and O(n) Moves

We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(n log n) element comparisons and O(n) element transports. This solves a long-standing open problem, stated explicitly, e.g., in [J.I. Munro and V. Raman, Sorting with minimum data movement, J. Algorithms, 13, 374-93, 1992], of whether there exists a sorting algorithm that matches the asymptotic lower bounds on all computational resources simultaneously

Sorting Stably, In-Place, with O(n log n) Comparisons and O(n) Moves

We settle a long-standing open question, namely whether it is possible to sort a sequence of n elements stably (i.e. preserving the original relative order of the equal elements), using O(1) auxiliary space and performing O(n log n) comparisons and O(n) data moves. Munro and Raman stated this problem in [J. Algorithms, 13, 1992] and gave an in-place but unstable sorting algorithm that performs O(n) data moves and O(n1+e) comparisons. Subsequently [Algorithmica, 16, 1996] they presented a stable algorithm with these same bounds. Recently, Franceschini and Geffert [FOGS 2003] presented an unstable sorting algorithm that matches the asymptotic lower bounds on all computational resources

Cadherin specificity in adhesion and mechanotransduction

Cadherins mediate Ca2+ dependent cell-cell junction in all animal tissues. Tight regulation of cadherin adhesion plays critical roles in diverse biological processes. Differential binding between cadherin subtypes is widely believed to mediate cell sorting during embryogenesis. However, a fundamental unanswered question is whether cell sorting is dictated by the biophysical properties of cadherin bonds. Chapter 2 describes the atomic force microscope measurements of the strengths and dissociation rates of homophilic and heterophilic cadherin bonds. Measurements conducted with chicken N-cadherin, canine E-cadherin, and Xenopus C-cadherin demonstrated that all three cadherins cross-react and form multiple, intermolecular bonds. The mechanical and kinetic properties of the heterophilic bonds are similar to the homophilic interactions. The quantified bond parameters, together with previously reported adhesion energies were further compared with in vitro cell aggregation and sorting assays. Trends in quantified biophysical properties of the different cadherin bonds do not correlate with sorting outcomes. These results suggest that cell sorting in vivo and in vitro is not governed solely by biophysical differences between cadherin subtypes. Although the knowledge of molecular mechanism of cadherin adhesion is fundamental to understanding various processes in morphogenesis and the regulation of cell junctions, it remains largely unclear. In Chapter 3, single bond force measurement was used to directly address the functional roles of Trp2 and adhesive domains in C-cadherin interaction. The bond rupture forces between the cadherin ectodomains, domain deletion fragments, and Trp2 point mutant were measured and compared. The results, together with surface force measurements (Maruthamuthu, Ph.D thesis 2009) demonstrated that Trp2 residue both mediates the N-terminal interaction of cadherins and exerts an inter-domain allosteric effect on multiple domains far away from EC1. The findings of the allosteric coupling between classic cadherin ectodomains reconcile several previous models of cadherin adhesion and may have important implications for the regulation of cadherin-based cell adhesion. The importance of mechanical force to development, differentiation, and normal physiology is increasingly acknowledged. Although the classic cadherin complex is a good candidate for tension sensing in tissues, direct evidence for such a role is lacking. In Chapter 4, I examined the cell responses to both external applied forces and soft substrates via classic type I cadherins. Cells respond to applied force through cadherin bonds by reinforcing the bead-cell junction, showing cadherin complexes are force-sensors. Besides, depending on cell context, the cadherin mechanotransduction is subtype-specific. To study how cells respond to passive substrate rigidity, MCF-7 cell spreading on soft gels coated with E-cadherins was examined. The spreading area of cells increases with substrate rigidity. This behavior indicates that the cells are able to sense the substrate stiffness through cadherin receptors and modify their spreading accordingly. These results provide direct evidences that cadherins complexes are mechanosensors

Dynamics and parameterization of stably stratified turbulence: implications for estimates of mixing in geophysical flows

2014 Summer.Includes bibliographical references.This research focuses on the relationship between the observed length scales of overturns in stably-stratified shear-flow turbulence and the fundamental length scales constructed from dimensional analysis of basic physical quantities. In geophysical flows such as the ocean, overturns are relatively easy to observe while the basic quantities are not. As such, overturns provide a means of inferring basic quantities if the relationship between the observed and fundamental scales are known. In turn, inferred values of the basic quantities, namely the the turbulent kinetic energy k, and the dissipation rate of turbulent kinetic energy ϵ, can be used to estimate diapycnal diffusivity (i.e. turbulent mixing). Most commonly, the observed Thorpe length scale, LT, is assumed to scale linearly with the fundamental Ozmidov scale, LO =(ϵ/N3)1/2, so that inferred values of ϵ can be obtained and used to estimate mixing from the Osborn formulation for diapycnal diffusivity. A major goal of this research is to re-examine this and other possible scalings using dimensional analysis, direct numerical simulation (DNS), laboratory data, and field observations. The preliminary chapters constitute a fresh approach at dimensional analysis that presents the fundamental length scales, time scales, and dimensionless parameters relevant to the problem. The relationship between LT and the fundamental length scales is then examined for the simple case of homogeneously stratified turbulence (without shear) using DNS. A key finding is that the common practice of inferring ϵ from LT ~ LO, is valid at the transition between a buoyancy-dominated regime and an inertia-dominated regime where the time scale of the buoyancy oscillations, N-1, roughly matches that of the inertial motions, TL = k/ϵ. Regime definition is made possible using a non-dimensional buoyancy strength parameter NTL = Nk/ϵ. Next, the problem is generalized to consider mean shear, and thus, a shear strength parameter, STL = Sk/ϵ, and the gradient Richardson number, Ri = N2/S2, are considered along with NTL to define three regimes available to high Reynolds number stratified shear-flow turbulence: a buoyancy-dominated regime (NTL ≳ 1.7, Ri ≳ 0.25), a shear-dominated regime (STL ≳ 3.3, Ri ≲ 0.25), and an inertia-dominated regime (NTL ≲ 1.7, STL ≲ 3.3). The regimes constitute a multi-dimensional parameter space which elucidates the independent influences that shear and stratification have on the turbulence. Using a large database of DNS and laboratory results, overturns are shown to have unique scalings in the various regimes. Specifically, LT ~ k1/2N-1, LT ~ k1/2S-1, and LT ~ k3/2ϵ-1 in the buoyancy-, shear-, and inertia-dominated regimes, respectively. LT ~ LO is found only for the case of NTL = O(1) and STL ≲ 3.3, or for NTL = O(100), STL ≈ 3.3 and Ri ≈ 0.25 when shear is present. In all three regimes, LT is found to generally indicate k rather than ϵ. An alternative parameterization of turbulent diffusivity is developed based on inferred values of k with a practical eye toward field applications. When tested with DNS and laboratory data, the new model is shown to be more accurate than estimates based on inferred values of ϵ. The multi-parameter framework is broadened with consideration for the turbulent Reynolds number, ReL, thus allowing for an evaluation of existing parameterizations of diapycnal mixing efficiency, R*f. Select DNS and laboratory data sets are used in the analysis. A key finding is that descriptions of R*f based on a single-parameter are generally insufficient. It is found that Ri is an accurate parameter in the shear-dominated regime but fails in the inertia-dominated regime where turbulence is generated by external forcing (rather than mean shear). In contrast, the turbulent Froude number, FrT = (LO/LT)2/3, is an accurate parameter in the inertia-dominated regime but loses accuracy in the shear-dominated regime. Neither Ri or FrT sufficiently describe R*f in the buoyancy-dominated regime where additional consideration for ReL is needed. Another key finding is that the popular buoyancy Reynolds number, Reb = ReL(NTL)-2, is a particularly misleading parameter for describing R*f because it fails to distinguish between (i) a low-Reynolds number, weakly stratified regime of low efficiency (low ReL, low NTL, low R*f) typical of DNS flows and (ii) a high-Reynolds number, strongly stratified regime of high efficiency (high ReL, high NTL, high R*f) typical of geophysical flows. Finally, oceanic observations from Luzon Strait and the Brazil Basin are featured to examine the relationship between LT and LO in geophysical flows where turbulence is driven by overturns that are very large by open ocean standards. LT is found to increase with respect to LO as a function of the normalized overturn size LT = LTN1/2ν-1/2. When large overturns are present, dissipation rates inferred from LT ~ LO are generally larger than measured values on average. The overestimation is quantified over a spring tidal period at Luzon Strait where depth- and time-integration of inferred and measured values show that inferred energy dissipation is four times too large

Foundations of Differentially Oblivious Algorithms

It is well-known that a program\u27s memory access pattern can leak information about its input. To thwart such leakage, most existing works adopt the solution of oblivious RAM (ORAM) simulation. Such a notion has stimulated much debate. Some have argued that the notion of ORAM is too strong, and suffers from a logarithmic lower bound on simulation overhead. Despite encouraging progress in designing efficient ORAM algorithms, it would nonetheless be desirable to avoid the oblivious simulation overhead. Others have argued that obliviousness, without protection of length-leakage, is too weak, and have demonstrated examples where entire databases can be reconstructed merely from length-leakage. Inspired by the elegant notion of differential privacy, we initiate the study of a new notion of access pattern privacy, which we call ``$(\epsilon, \delta)$-differential obliviousness\u27\u27. We separate the notion of $(\epsilon, \delta)$-differential obliviousness from classical obliviousness by considering several fundamental algorithmic abstractions including sorting small-length keys, merging two sorted lists, and range query data structures (akin to binary search trees). We show that by adopting differential obliviousness with reasonable choices of $\epsilon$ and $\delta$, not only can one circumvent several impossibilities pertaining to the classical obliviousness notion, but also in several cases, obtain meaningful privacy with little overhead relative to the non-private baselines (i.e., having privacy ``almost for free\u27\u27). On the other hand, we show that for very demanding choices of $\epsilon$ and $\delta$, the same lower bounds for oblivious algorithms would be preserved for $(\epsilon, \delta)$-differential obliviousness

Novel Mechanisms Regulating Dopamine Transporter Endocytic Trafficking: Ack1-Controlled Endocytosis And Retromer-Mediated Recycling

Dopamine transporters (DAT) facilitate high-affinity presynaptic dopamine (DA) reuptake in the central nervous system, and are required to constrain extracellular DA levels and maintain presynaptic DAergic tone. DAT is the primary target for addictive and therapeutic psychostimulants, which require DAT binding to elicit reward. DAT availability at presynaptic terminals ensures its proper function, and is dynamically regulated by endocytic trafficking. My thesis research focused on two fundamental questions: 1) what are the molecular mechanisms that control DAT endocytosis? and 2) what are the mechanism(s) that govern DAT’s post-endocytic fate? Using pharmacological and genetic approaches, I discovered that a non-receptor tyrosine kinase, activated by cdc42 kinase 1 (Ack1), stabilizes DAT plasma membrane expression by negatively regulating DAT endocytosis. I found that stimulated DAT endocytosis absolutely requires Ack1 inactivation. Moreover, I was able to restore normal DAT endocytosis to a trafficking dysregulated DAT coding variant identified in an Attention Deficit Hyperactivity Disorder (ADHD) patient via constitutively activating Ack1. To address what mechanisms govern DAT’s post-endocytic fate, I took advantage of a small molecule labeling approach to directly couple fluorophore to the DAT surface population, and subsequently tracked DAT’s temporal-spatial post-endocytic itinerary in immortalized mesencephalic cells. Using this approach, I discovered that the retromer complex mediates DAT recycling and is required to maintain DAT surface levels via a DAT C-terminal PDZ-binding motif. Taken together, these findings shed considerable new light on DAT trafficking mechanisms, and pave the way for future studies examining the role of regulated DAT trafficking in neuropsychiatric disorders

Structural Concept Learning via Graph Attention for Multi-Level Rearrangement Planning

Robotic manipulation tasks, such as object rearrangement, play a crucial role in enabling robots to interact with complex and arbitrary environments. Existing work focuses primarily on single-level rearrangement planning and, even if multiple levels exist, dependency relations among substructures are geometrically simpler, like tower stacking. We propose Structural Concept Learning (SCL), a deep learning approach that leverages graph attention networks to perform multi-level object rearrangement planning for scenes with structural dependency hierarchies. It is trained on a self-generated simulation data set with intuitive structures, works for unseen scenes with an arbitrary number of objects and higher complexity of structures, infers independent substructures to allow for task parallelization over multiple manipulators, and generalizes to the real world. We compare our method with a range of classical and model-based baselines to show that our method leverages its scene understanding to achieve better performance, flexibility, and efficiency. The dataset, supplementary details, videos, and code implementation are available at: https://manavkulshrestha.github.io/sclComment: Accepted to Conference on Robot Learning (CoRL) 202