No-signaling Linear PCPs

In this paper, we give a no-signaling linear probabilistically checkable proof (PCP) system for polynomial-time deterministic computation, i.e., a PCP system for P such that (1) the honest PCP oracle is a linear function and (2) the soundness holds against any (computational) no-signaling cheating prover, who is allowed to answer each query according to a distribution that depends on the entire query set in a certain way. To the best of our knowledge, our construction is the first PCP system that satisfies these two properties simultaneously. As an application of our PCP system, we obtain a 2-message delegating computation scheme by using a known transformation. Compared with the existing 2-message delegating computation schemes that are based on standard cryptographic assumptions, our scheme requires preprocessing but has a simpler structure and makes use of different (possibly cheaper) standard cryptographic primitives, namely additive/multiplicative homomorphic encryption schemes

On Local Testability in the Non-Signaling Setting

Non-signaling strategies are a generalization of quantum strategies that have been studied in physics for decades, and have recently found applications in theoretical computer science. These applications motivate the study of local-to-global phenomena for non-signaling functions. We prove that low-degree testing in the non-signaling setting is possible, assuming that the locality of the non-signaling function exceeds a threshold. We additionally show that if the locality is below the threshold then the test fails spectacularly, in that there exists a non-signaling function which passes the test with probability 1 and yet is maximally far from being low-degree. Along the way, we present general results about the local testability of linear codes in the non-signaling setting. These include formulating natural definitions that capture the condition that a non-signaling function "belongs" to a given code, and characterizing the sets of local constraints that imply membership in the code. We prove these results by formulating a logical inference system for linear constraints on non-signaling functions that is complete and sound

Probabilistic Checking Against Non-Signaling Strategies from Linearity Testing

Non-signaling strategies are a generalization of quantum strategies that have been studied in physics over the past three decades. Recently, they have found applications in theoretical computer science, including to proving inapproximability results for linear programming and to constructing protocols for delegating computation. A central tool for these applications is probabilistically checkable proofs (PCPs) that are sound against non-signaling strategies. In this paper we prove that the exponential-length constant-query PCP construction due to Arora et al. (JACM 1998) is sound against non-signaling strategies. Our result offers a new length-vs-query tradeoff when compared to the non-signaling PCP of Kalai, Raz, and Rothblum (STOC 2013 and 2014) and, moreover, may serve as an intermediate step to a proof of a non-signaling analogue of the PCP Theorem

Toward probabilistic checking against non-signaling strategies with constant locality

Non-signaling strategies are a generalization of quantum strategies that have been studied in physics over the past three decades. Recently, they have found applications in theoretical computer science, including to proving inapproximability results for linear programming and to constructing protocols for delegating computation. A central tool for these applications is probabilistically checkable proof (PCPs) systems that are sound against non-signaling strategies. In this thesis we show, assuming a certain geometrical hypothesis about noise robustness of non-signaling proofs (or, equivalently, about robustness to noise of solutions to the Sherali-Adams linear program), that a slight variant of the parallel repetition of the exponential-length constant-query PCP construction due to Arora et al. (JACM 1998) is sound against non-signaling strategies with constant locality. Our proof relies on the analysis of the linearity test and agreement test (also known as the direct product test) in the non-signaling setting

Identification and Specification of the Mouse Skeletal Stem Cell

SummaryHow are skeletal tissues derived from skeletal stem cells? Here, we map bone, cartilage, and stromal development from a population of highly pure, postnatal skeletal stem cells (mouse skeletal stem cells, mSSCs) to their downstream progenitors of bone, cartilage, and stromal tissue. We then investigated the transcriptome of the stem/progenitor cells for unique gene-expression patterns that would indicate potential regulators of mSSC lineage commitment. We demonstrate that mSSC niche factors can be potent inducers of osteogenesis, and several specific combinations of recombinant mSSC niche factors can activate mSSC genetic programs in situ, even in nonskeletal tissues, resulting in de novo formation of cartilage or bone and bone marrow stroma. Inducing mSSC formation with soluble factors and subsequently regulating the mSSC niche to specify its differentiation toward bone, cartilage, or stromal cells could represent a paradigm shift in the therapeutic regeneration of skeletal tissues

Towards a molecular mechanism underlying mitochondrial protein import through the TOM and TIM23 complexes

Nearly all mitochondrial proteins need to be targeted for import from the cytosol. For the majority, the first port of call is the translocase of the outer membrane (TOM complex), followed by a procession of alternative molecular machines, conducting transport to their final destination. The pre-sequence translocase of the inner membrane (TIM23-complex) imports proteins with cleavable pre-sequences. Progress in understanding these transport mechanisms has been hampered by the poor sensitivity and time resolution of import assays. However, with the development of an assay based on split NanoLuc luciferase, we can now explore this process in greater detail. Here, we apply this new methodology to understand how ∆ψ and ATP hydrolysis, the two main driving forces for import into the matrix, contribute to the transport of pre-sequence-containing precursors (PCPs) with varying properties. Notably, we found that two major rate-limiting steps define PCP import time: passage of PCP across the outer membrane and initiation of inner membrane transport by the pre-sequence – the rates of which are influenced by PCP size and net charge. The apparent distinction between transport through the two membranes (passage through TOM is substantially complete before PCP-TIM engagement) is in contrast with the current view that import occurs through TOM and TIM in a single continuous step. Our results also indicate that PCPs spend very little time in the TIM23 channel – presumably rapid success or failure of import is critical for maintenance of mitochondrial fitness

Environmental chemical exposures and breast cancer

As a hormone-sensitive condition with no single identifiable cause, breast cancer is a major health problem. It is characterized by a wide range of contributing factors and exposures occurring in different combinations and strengths across a lifetime that may be amplified during periods of enhanced developmental susceptibility and impacted by reproductive patterns and behaviours. The vast majority of cases are oestrogen-receptor positive and occur in women with no family history of the disease suggesting that modifiable risk factors are involved. A substantial body of evidence now links oestrogen-positive breast cancer with environmental exposures. Synthetic chemicals capable of oestrogen mimicry are characteristic of industrial development and have been individually and extensively assessed as risk factors for oestrogen-sensitive cancers. Existing breast cancer risk assessment tools do not take such factors into account. In the absence of consensus on causation and in order to better understand the problem of escalating incidence globally, an expanded, integrated approach broadening the inquiry into individual susceptibility breast cancer is proposed. Applying systems thinking to existing data on oestrogen-modulating environmental exposures and other oestrogenic factors characteristic of Westernisation and their interactions in the exposure, encompassing social, behavioural, environmental, hormonal and genetic factors, can assist in understanding cancer risks and the pursuit of prevention strategies. A new conceptual framework based on a broader understanding of the “system” that underlies the development of breast cancer over a period of many years, incorporating the factors known to contribute to breast cancer risk, could provide a new platform from which government and regulators can promulgate enhanced and more effective prevention strategies