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The topic of diversity is an interesting subject, both as a purely mathematical concept and also for its applications to important real-life situations. Unfortunately, although the meaning of diversity seems intuitively clear, no precise…
The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop…
This is a philosophical paper. It claims that there is a gap to be filled in the relationship between complexity theory (CT) and quantum theory (QT). This gap concerns two very distinct understandings of time. The paper provides the ground…
We explore two distinct resolutions to the tachyonic slepton puzzle in the Anomaly Mediated Supersymmetry Breaking scenario. Both are based on extending the MSSM by an anomaly free U(1) symmetry, and in both cases exact RG invariance is…
The Multiverse is collection of parallel universes. In this article a formal theory and a topos-theoretic models of the multiverse are given. For this the Lawvere-Kock Synthetic Differential Geometry and topos models for smooth…
We review a few off-the-beaten-track ideas in cosmology. They solve a variety of fundamental problems; also they are fun. We start with a description of non-singular dilaton cosmology. In these scenarios gravity is modified so that the…
Resolution of the cosmological constant problem based on Causal Set theory is discussed. It is argued that one should not observe any spacetime variations in cosmological constant if Causal Set approach is correct.
The goal of this work is to prove a new sure upper bound in a setting that can be thought of as a simplified function field analogue. This result is comparable to a recent result of the author concerning almost sure upper bound of random…
It is argued that the traditional "realist" methodology of physics, according to which human concepts, laws and theories can grasp the essence of reality, is incompatible with the most fruitful interpretation of quantum formalism. The proof…
Modern and anticipated facilities will deliver data that promises to reveal the innermost workings of quantum chromodynamics (QCD). In order to fulfill that promise, phenomenology and theory must reach a new level, limiting and overcoming…
We develop a data-driven approach to the computation of a-posteriori feasibility certificates to the solution sets of variational inequalities affected by uncertainty. Specifically, we focus on instances of variational inequalities with a…
We analyze the realm of validity of the recently found tachyon solution of cubic string field theory. We find that the equation of motion holds in a non trivial way when this solution is contracted with itself. This calculation is needed to…
We consider quantum search on graphs. Recently, it has been shown that the graph properties like connectivity, global symmetry, or regularity cannot serve as a reliable criteria that must be satisfied by a graph to allow a successful…
It will be argued here that the cosmological constant problem exists because of the way the vacuum is defined in quantum field theory. It has been known for some time that for QFT to be gauge invariant certain terms--such as part of the…
Despite numerous attempts at mitigation since the inception of language models, hallucinations remain a persistent problem even in today's frontier LLMs. Why is this? We review existing definitions of hallucination and fold them into a…
Hallucinations, a phenomenon where a language model (LM) generates nonfactual content, pose a significant challenge to the practical deployment of LMs. While many empirical methods have been proposed to mitigate hallucinations, recent…
We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. A wide…
Like Asynchrony, Mobility of faults precludes consensus. Yet, a model M in which Consensus is solvable, has an analogue relaxed model in which Consensus is not solvable and for which we can ask, whether Consensus is solvable if the system…
The mystery of the cosmological constant is probably the most pressing obstacle to significantly improving the models of elementary particle physics derived from string theory. The problem arises because in the standard framework of low…
A quantum theory of the universe consists of a theory of its quantum dynamics and a theory of its quantum state The theory predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the…