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Niladri Sarkar

Publications and source records attributed to Niladri Sarkar.

At least 19 recordsLinked to original sources

Unlearning or Concealment? A Critical Analysis and Evaluation Metrics for Unlearning in Diffusion Models

Recent research has seen significant interest in methods for concept removal and targeted forgetting in text-to-image diffusion models. In this paper, we conduct a comprehensive white-box analysis showing the vulnerabilities in existing diffusion model unlearning methods. We show that existing unlearning methods lead to decoupling of the targeted concepts (meant to be forgotten) for the corresponding prompts. This is concealment and not actual forgetting, which was the original goal. This paper presents a rigorous theoretical and empirical examination of five commonly used techniques for unlearning in diffusion models, while showing their potential weaknesses. We introduce two new evaluation metrics: Concept Retrieval Score (\textbf{CRS}) and Concept Confidence Score (\textbf{CCS}). These metrics are based on a successful adversarial attack setup that can recover \textit{forgotten} concepts from unlearned diffusion models. \textbf{CRS} measures the similarity between the latent representations of the unlearned and fully trained models after unlearning. It reports the extent of retrieval of the \textit{forgotten} concepts with increasing amount of guidance. CCS quantifies the confidence of the model in assigning the target concept to the manipulated data. It reports the probability of the \textit{unlearned} model's generations to be aligned with the original domain knowledge with increasing amount of guidance. The \textbf{CCS} and \textbf{CRS} enable a more robust evaluation of concept erasure methods. Evaluating existing five state-of-the-art methods with our metrics, reveal significant shortcomings in their ability to truly \textit{unlearn}. Source Code: \color{blue}{https://respailab.github.io/unlearning-or-concealment}

cs.LG

Transport properties in a two-dimensional Su-Schrieffer-Heeger model in Quantum Hall Regime

We investigate the transport properties of a two-dimensional Su-Schrieffer-Heeger (2D SSH) model in the quantum Hall regime using non-equilibrium Green's function formalism (NEGF). The device Hamiltonian, where the 2D SSH model serves as the channel, is constructed using a nearest-neighbor tight-binding model. The effect of an external perpendicular magnetic field is incorporated into the contacts via Peierls substitution. We observe a transition from a gapped phase to a flat band regime at zero energy by varying the magnetic field. This transition is characterized by the emergence of highly localized states in the bulk or edges, which we observe by calculating local density-of-states (LDOS). We analyze transport in the system along two directions ($x$ and $y$) via transmission measurements, indicating a magnetic field-induced transition from insulating to metallic phase. The study of the energy spectrum of the system shows the formation of Landau levels. Moreover, the quantum number of the non-degenerate and degenerate Landau levels (transmission modes) can be any integer or only an odd integer, depending on diagonal, inter-cell, and intra-cell hopping strengths. From the analysis of the transport properties along $y$-direction, we find that edge modes play a crucial role in facilitating ballistic transport.

cond-mat.mes-hall

Long-ranged order and flow alignment in sheared $p-$atic liquid crystals

We formulate a hydrodynamic theory of $p-$atic liquid crystals, namely two-dimensional anisotropic fluids endowed with generic $p-$fold rotational symmetry. Our approach, based on an order parameter tensor that directly embodies the discrete rotational symmetry of $p-$atic phases, allows us to unveil several unknown aspects of flowing $p-$atics, that previous theories, characterized by ${\rm O(2)}$ rotational symmetry, could not account for. This includes the onset of long-ranged orientational order in the presence of a simple shear flow of arbitrary shear rate, as opposed to the standard quasi-long-ranged order of two-dimensional liquid crystals, and the possibility of flow alignment at large shear rates.

cond-mat.soft

Hydrodynamic theory of flocking at a solid-liquid interface: long range order and giant number fluctuations

We construct the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface. The polar order parameter and concentration of a collection of "active" (self-propelled) particles at a planar interface between a passive, isotropic bulk fluid and a solid surface are dynamically coupled to the bulk fluid. We find that such systems are stable, and have long-range orientational order, over a wide range of parameters. When stable, these systems exhibit "giant number fluctuations", i.e., large fluctuations of the number of active particles in a fixed large area. Specifically, these number fluctuations grow as the $3/4$th power of the mean number within the area. Stable systems also exhibit anomalously rapid diffusion of tagged particles suspended in the passive fluid along any directions in a plane parallel to the solid-liquid interface, whereas the diffusivity along the direction perpendicular to the plane is non-anomalous. In other parameter regimes, the system becomes unstable.

cond-mat.soft

Swarming bottom feeders: Flocking at solid-liquid interfaces

We present the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface, and many of its predictions for experiment. We find that such systems are stable, and have long-range orientational order, over a wide range of parameters. When stable, these systems exhibit "giant number fluctuations", which grow as the 3/4th power of the mean number. Stable systems also exhibit anomalous rapid diffusion of tagged particles suspended in the passive fluid along any directions in a plane parallel to the solid-liquid interface, whereas the diffusivity along the direction perpendicular to the plane is not anomalous. In the remaining parameter space, the system becomes unstable.

cond-mat.soft

Hydrodynamic theory of $p-$atic liquid crystals

We formulate a comprehensive hydrodynamic theory of two-dimensional liquid crystals with generic $p-$fold rotational symmetry, also known as $p-$atics, of which mematics $(p=2)$ and hexatics $(p=6)$ are the two best known examples. Previous hydrodynamic theories of $p-$atics are characrerized by continuous ${\rm O}(2)$ rotational symmetry, which is higher than the discrete rotational symmetry of $p-$atic phases. By contrast, here we demonstrate that the discrete rotational symmetry allows the inclusion of additional terms in the hydrodynamic equations, which, in turn, lead to novel phenomena, such as the possibility of flow alignment at high shear rates, even for $p>2$. Furthermore, we show that any finite imposed shear will induce long-ranged orientational order in any $p-$atic liquid crystal, in contrast to the quasi-long-ranged order that occurs in the absence of shear. The induced order parameter scales like a non-universal power of the applied shear rate at small shear rates.

cond-mat.soft

Fluid pumping and active flexoelectricity can promote lumen nucleation in cell assemblies

We discuss the physical mechanisms that promote or suppress the nucleation of a fluid-filled lumen inside a cell assembly or a tissue. We discuss lumen formation in a continuum theory of tissue material properties in which the tissue is described as a two-fluid system to account for its permeation by the interstitial fluid, and we include fluid pumping as well as active electric effects. Considering a spherical geometry and a polarized tissue, our work shows that fluid pumping and tissue flexoelectricity play a crucial role in lumen formation. We furthermore explore the large variety of long-time states that are accessible for the cell aggregate and its lumen. Our work reveals a role of the coupling of mechanical, electrical and hydraulic phenomena in tissue lumen formation.

physics.bio-ph

Topotaxis of active Brownian particles

Recent experimental studies have demonstrated that cellular motion can be directed by topographical gradients, such as those resulting from spatial variations in the features of a micropatterned substrate. This phenomenon, known as topotaxis, is especially prominent among cells persistently crawling within a spatially varying distribution of cell-sized obstacles. In this article we introduce a toy model of topotaxis based on active Brownian particles constrained to move in a lattice of obstacles, with space-dependent lattice spacing. Using numerical simulations and analytical arguments, we demonstrate that topographical gradients introduce a spatial modulation of the particles' persistence, leading to directed motion toward regions of higher persistence. Our results demonstrate that persistent motion alone is sufficient to drive topotaxis and could serve as a starting point for more detailed studies on self-propelled particles and cells.

cond-mat.soft

Rolled up or crumpled: phases of asymmetric tethered membranes

We show that inversion-asymmetric tethered membranes exhibit a new double-spiral phase with long range orientational order not present in symmetric membranes. We calculate the universal algebraic spiral shapes of these membranes in this phase. Asymmetry can trigger the crumpling of these membranes as well. In-vitro experiments on lipid, red blood cell membrane extracts, and on graphene coated on one side, could test these predictions.

cond-mat.stat-mech

Statistical mechanics of asymmetric tethered membranes: spiral and crumpled phases

We develop the elastic theory for inversion-asymmetric tethered membranes and use it to identify and study their possible phases. Asymmetry in a tethered membrane causes spontaneous curvature, which in general depends upon the local in-plane dilation of the tethered network. This in turn leads to long-ranged interactions between the local mean and Gaussian curvatures, which is not present in symmetric tethered membranes. This interplay between asymmetry and Gaussian curvature leads to a new {\em double-spiral} phase not found in symmetric tethered membranes. At temperature $T=0$, tethered membranes of arbitrarily large size are always rolled up tightly into a conjoined pair of Archimedes' spirals. At finite $T$ this spiral structure swells up significantly into algebraic spirals characterized by universal exponents which we calculate. These spirals have long range orientational order, and are the asymmetric analogs of statistically flat symmetric tethered membranes. We also find that sufficiently strong asymmetry can trigger a structural instability leading to crumpling of these membranes as well. This provides a new route to crumpling for asymmetric tethered membranes. We calculate the maximum linear extent $L_c$ beyond which the membrane crumples, and calculate the universal dependence of $L_c$ on the membrane parameters. By tuning the asymmetry parameter, $L_c$ can be continuously varied, implying a {\em scale-dependent} crumpling. Our theory can be tested on controlled experiments on lipids with artificial deposits of spectrin filaments, in-vitro experiments on %\sout{artificial deposition of spectrin filaments on} red blood cell membrane extracts, %\sout{after %depletion of adenosine-tri-phosphate molecules} and on graphene coated on one side.

cond-mat.stat-mech

Field induced cell proliferation and death in a thick epithelium

We study the dynamics of a thick polar epithelium subjected to the action of both an electric and a flow field in a planar geometry. We develop a generalized continuum hydrodynamic description and describe the tissue as a two component fluid system. The cells and the interstitial fluid are the two components and we keep all terms allowed by symmetry. In particular we keep track of the cell pumping activity for both solvent flow and electric current and discuss the corresponding orders of magnitude. We study the growth dynamics of tissue slabs, their steady states and obtain the dependence of the cell velocity, net cell division rate, and cell stress on the flow strength and the applied electric field. We find that finite thickness tissue slabs exist only in a restricted region of phase space and that relatively modest electric fields or imposed external flows can induce either proliferation or death.

q-bio.CB

Tethered membranes do not remain flat for strong structural asymmetry

We set up the statistical mechanics for a nearly flat, thermally equilibrated fluid membrane, attached to an elastic network through one of its sides. We predict that the resulting structural (inversion) asymmetry of the membrane, notably due to the elastic network attached to one of its sides, can generate a local spontaneous curvature $C_0$, that may in turn destabilize the otherwise flat membrane. As $C_0$ rises above a threshold at a fixed temperature, a flat tethered membrane in the thermodynamic limit becomes structurally unstable, signaling {\em crumpling} of the flat membrane. In-vitro experiments on red blood cell membranes after depletion of adenosine-tri-phosphate molecules and artificial deposition of spectrin filaments on lipid bilayers may be used to verify our results.

cond-mat.soft

The analogue Hawking effect in rotating polygonal hydraulic jumps

Rotation of non-circular hydraulic jumps is a recent experimental observation that lacks a theory based on first principles. Here we furnish a basic theory of this phenomenon founded on the shallow-water model of the circular hydraulic jump. The breaking of the axial symmetry morphs the circular jump into a polygonal state. Variations on this state rotate the polygon in the azimuthal direction. The dependence of the rotational frequency on the flow rate and on the number of polygon vertices agrees with known experimental results. We also predict how the rotational frequency varies with viscosity. Finally, we establish a correspondence between the rotating polygonal structure and the Hawking effect in an analogue white hole. The rotational frequency of the polygons affords a direct estimate of the frequency of the thermal Hawking radiation.

physics.flu-dyn

Phase transitions and order in two-dimensional generalized nonlinear $σ$-models

We study phase transitions and the nature of order in a class of classical generalized $O(N)$ nonlinear $σ$-models (NLS) constructed by minimally coupling pure NLS with additional degrees of freedom in the form of (i) Ising ferromagnetic spins, (ii) an advective Stokesian velocity and (iii) multiplicative noises. In examples (i) and (ii), and also (iii) with the associated multiplicative noise being not sufficiently long-ranged, we show that the models may display a class of unusual phase transitions between {\em stiff} and {\em soft phases}, where the effective spin stiffness, respectively, diverges and vanishes in the long wavelength limit at two dimensions ($2d$), unlike in pure NLS. In the stiff phase, in the thermodynamic limit the variance of the transverse spin (or, the Goldstone mode) fluctuations are found to scale with the system size $L$ in $2d$ as $\ln\ln L$ with a model-dependent amplitude, that is markedly weaker than the well-known $\ln L$-dependence of the variance of the broken symmetry modes in models that display quasi-long range order in $2d$. Equivalently, for $N=2$ at $2d$ the equal-time spin-spin correlations decay in powers of inverse logarithm of the spatial separation with model-dependent exponents. These transitions are controlled by the model parameters those couple the $O(N)$ spins with the additional variables. In the presence of long-range noises in example (iii), true long-range order may set in $2d$, depending upon the specific details of the underlying dynamics. Our results should be useful in understanding phase transitions in equilibrium and nonequilibrium low-dimensional systems with continuous symmetries in general.

cond-mat.stat-mech

Role of interfacial friction for flow instabilities in a thin polar ordered active fluid layer

We construct a generic coarse-grained dynamics of a thin inflexible planar layer of polar-ordered suspension of active particles, that is frictionally coupled to an embedding isotropic passive fluid medium with a friction coefficient $Γ$. Being controlled by $Γ$, our model provides a unified framework to describe the long wavelength behaviour of a variety of thin polar-ordered systems, ranging from {\em wet} to {\em dry} active matters and free standing active films. Investigations of the linear instabilities around a chosen orientationally ordered uniform reference state reveal generic moving and static instabilities in the system, that can depend sensitively on $Γ$. Based on our results, we discuss estimation of bounds on $Γ$ in experimentally accessible systems.

cond-mat.soft

Active-to-absorbing-state phase transition in an evolving population with mutation

We study the active to absorbing phase transition (AAPT) in a simple two-component model system for a species and its mutant. We uncover the nontrivial critical scaling behavior and weak dynamic scaling near the AAPT that shows the significance of mutation and highlights the connection of this model with the well-known directed percolation universality class. Our model should be a useful starting point to study how mutation may affect extinction or survival of a species.

cond-mat.stat-mech

Phase transitions and membrane stiffness in a class of asymmetric heterogeneous fluid membranes

We propose a minimal model for miscibility phase transitions (MPTs) in a class of asymmetric two-component heterogeneous fluid membranes at equilibrium that generically display both first and second order MPTs, controlled by the interplay of asymmetry and heterogeneity. In the vicinity of the MPTs, the membrane fluctuations are generally enhanced. However, the degree of enhancement is found to depend sensitively on the asymmetry-heterogeneity coupling. We argue that experimental measurements of the membrane fluctuations at the MPTs should provide physical information about the forms of the asymmetry-heterogeneity couplings.

cond-mat.soft

Generic nonequilibrium steady states in an exclusion process on an inhomogeneous ring

We consider a one-dimensional totally asymmetric exclusion process on a ring with extended inhomogeneities, consisting of several segments with different hopping rates. Depending upon the underlying inhomogeneity configurations and for moderate densities, our model displays both localised (LDW) and delocalised (DDW) domain walls and delocalisation transitions of LDWs in the steady states. Our results allow us to construct the possible steady state density profiles for an arbitrary number of segments with unequal hopping rates. We explore the scaling properties of the fluctuations of LDWs and DDWs.

cond-mat.stat-mech