arXiv subjects

Karthik H. Shankar

Publications and source records attributed to Karthik H. Shankar.

9 recordsLinked to original sources

arXiv2020

Negative votes to depolarize politics

The controversies around the 2020 US presidential elections certainly casts serious concerns on the efficiency of the current voting system in representing the people's will. Is the naive Plurality voting suitable in an extremely polarized political environment? Alternate voting schemes are gradually gaining public support, wherein the voters rank their choices instead of just voting for their first preference. However they do not capture certain crucial aspects of voter preferences like disapprovals and negativities against candidates. I argue that these unexpressed negativities are the predominant source of polarization in politics. I propose a voting scheme with an explicit expression of these negative preferences, so that we can simultaneously decipher the popularity as well as the polarity of each candidate. The winner is picked by an optimal tradeoff between the most popular and the least polarizing candidate. By penalizing the candidates for their polarization, we can discourage the divisive campaign rhetorics and pave way for potential third party candidates.

econ.TH↗

arXiv2020

Eternally oscillating zero energy Universe

The question of whether the universe is eternal or if it had a singular moment of creation is deeply intriguing. Although different versions of steady state and oscillatory models of eternal universe have been envisaged, empirical evidence suggests a singular moment of creation at the big bang. Here we analyze the oscillatory solutions for the universe in a modified theory of gravity THED (Torsion Hides Extra-Dimension) and evaluate them by fitting Type 1a supernovae redshift data. THED-gravity exactly mimics General Relativity at the kinematical level, while the modifications in its dynamical equations allow the universe to bounce between a minimum size and a maximum size with a zero average energy within each oscillation. The optimally fit oscillatory solutions correspond to a universe with (i) a small matter density requiring little to no dark matter, (ii) a significantly negative spatial curvature, (iii) a tiny negative dark energy. Alternatively, there exists non-oscillating solutions that appear as an ever-expanding universe from a single bounce preceded by a collapse from the infinite past. These ever-expanding solutions provide marginally better fits to the supernova redshift data, but require larger matter densities and positive dark energy along with a positive spatial curvature. A qualitative analysis of CMB power spectrum in the modified theory suggests a significant negative spatial curvature, which is in stark contrast to a near-zero curvature in the standard big bang theory. An independent constraint on the spatial curvature can further shed light on discriminating the ever expanding and oscillatory universe scenarios.

gr-qc↗

arXiv2017

Neural scaling laws for an uncertain world

Autonomous neural systems must efficiently process information in a wide range of novel environments, which may have very different statistical properties. We consider the problem of how to optimally distribute receptors along a one-dimensional continuum consistent with the following design principles. First, neural representations of the world should obey a neural uncertainty principle---making as few assumptions as possible about the statistical structure of the world. Second, neural representations should convey, as much as possible, equivalent information about environments with different statistics. The results of these arguments resemble the structure of the visual system and provide a natural explanation of the behavioral Weber-Fechner law, a foundational result in psychology. Because the derivation is extremely general, this suggests that similar scaling relationships should be observed not only in sensory continua, but also in neural representations of ``cognitive' one-dimensional quantities such as time or numerosity.

q-bio.NC↗

arXiv2017

Horizonless, singularity-free, compact shells satisfying NEC

Gravitational collapse singularities are undesirable, yet inevitable to a large extent in General Relativity. When matter satisfying null energy condition collapses to the extent a closed trapped surface is formed, a singularity is inevitable according to Penrose's singularity theorem. Since positive mass vacuum solutions are generally black holes with trapped surfaces inside the event horizon, matter cannot collapse to an arbitrarily small size without generating a singularity. However, in modified theories of gravity where positive mass vacuum solutions are naked singularities with no trapped surfaces, it is reasonable to expect that matter can collapse to an arbitrarily small size without generating a singularity. Here we examine this possibility in the context of a modified theory of gravity with torsion in an extra dimension. We study singularity-free static shell solutions to evaluate the validity of the null energy condition on the shell. We find that with sufficiently high pressure, matter can be collapsed to arbitrarily small size without violating the null energy condition and without producing a singularity.

gr-qc↗

arXiv2015

Neural mechanism to simulate a scale-invariant future timeline

Predicting future events, and their order, is important for efficient planning. We propose a neural mechanism to non-destructively translate the current state of memory into the future, so as to construct an ordered set of future predictions. This framework applies equally well to translations in time or in one-dimensional position. In a two-layer memory network that encodes the Laplace transform of the external input in real time, translation can be accomplished by modulating the weights between the layers. We propose that within each cycle of hippocampal theta oscillations, the memory state is swept through a range of translations to yield an ordered set of future predictions. We operationalize several neurobiological findings into phenomenological equations constraining translation. Combined with constraints based on physical principles requiring scale-invariance and coherence in translation across memory nodes, the proposition results in Weber-Fechner spacing for the representation of both past (memory) and future (prediction) timelines. The resulting expressions are consistent with findings from phase precession experiments in different regions of the hippocampus and reward systems in the ventral striatum. The model makes several experimental predictions that can be tested with existing technology.

q-bio.NC↗

arXiv2015

Generic construction of scale-invariantly coarse grained memory

Encoding temporal information from the recent past as spatially distributed activations is essential in order for the entire recent past to be simultaneously accessible. Any biological or synthetic agent that relies on the past to predict/plan the future, would be endowed with such a spatially distributed temporal memory. Simplistically, we would expect that resource limitations would demand the memory system to store only the most useful information for future prediction. For natural signals in real world which show scale free temporal fluctuations, the predictive information encoded in memory is maximal if the past information is scale invariantly coarse grained. Here we examine the general mechanism to construct a scale invariantly coarse grained memory system. Remarkably, the generic construction is equivalent to encoding the linear combinations of Laplace transform of the past information and their approximated inverses. This reveals a fundamental construction constraint on memory networks that attempt to maximize predictive information storage relevant to the natural world.

q-bio.NC↗

arXiv2013

Optimally fuzzy temporal memory

Any learner with the ability to predict the future of a structured time-varying signal must maintain a memory of the recent past. If the signal has a characteristic timescale relevant to future prediction, the memory can be a simple shift register---a moving window extending into the past, requiring storage resources that linearly grows with the timescale to be represented. However, an independent general purpose learner cannot a priori know the characteristic prediction-relevant timescale of the signal. Moreover, many naturally occurring signals show scale-free long range correlations implying that the natural prediction-relevant timescale is essentially unbounded. Hence the learner should maintain information from the longest possible timescale allowed by resource availability. Here we construct a fuzzy memory system that optimally sacrifices the temporal accuracy of information in a scale-free fashion in order to represent prediction-relevant information from exponentially long timescales. Using several illustrative examples, we demonstrate the advantage of the fuzzy memory system over a shift register in time series forecasting of natural signals. When the available storage resources are limited, we suggest that a general purpose learner would be better off committing to such a fuzzy memory system.

cs.AI↗

arXiv2012

A metric theory of gravity with torsion in extra-dimension

We consider a theory of gravity with a hidden extra-dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra-dimension and the extra-dimension stays hidden at the level of four dimensional geodesic motion. At the kinematic level, the theory maps on to General Relativity, but the dynamical field equations that follow from the action principle deviate markedly from the standard Einstein equations. We study static spherically symmetric vacuum solutions and homogeneous-isotropic cosmological solutions that emerge from the field equations. In both cases, we find solutions of significant physical interest. Most notably, we find positive mass solutions with naked singularity that match the well known Schwarzschild solution at large distances but lack an event horizon. In the cosmological context, we find oscillatory scenario in contrast to the inevitable, singular big bang of the standard cosmology.

gr-qc↗

arXiv2010

Kaluza-Klein Theory with Torsion confined to the Extra-dimension

Here we consider a variant of the 5 dimensional Kaluza-Klein theory within the framework of Einstein-Cartan formalism that includes torsion. By imposing a set of constraints on torsion and Ricci rotation coefficients, we show that the torsion components are completely expressed in terms of the metric. Moreover, the Ricci tensor in 5D corresponds exactly to what one would obtain from torsion-free general relativity on a 4D hypersurface. The contributions of the scalar and vector fields of the standard K-K theory to the Ricci tensor and the affine connections are completely nullified by the contributions from torsion. As a consequence, geodesic motions do not distinguish the torsion free 4D space-time from a hypersurface of 5D space-time with torsion satisfying the constraints. Since torsion is not an independent dynamical variable in this formalism, the modified Einstein equations are different from those in the general Einstein-Cartan theory. This leads to important cosmological consequences such as the emergence of cosmic acceleration.

gr-qc↗