The Complexity of Fixed-Height Patterned Tile Self-Assembly

We characterize the complexity of the PATS problem for patterns of fixed height and color count in variants of the model where seed glues are either chosen or fixed and identical (so-called non-uniform and uniform variants). We prove that both variants are NP-complete for patterns of height 2 or more and admit O(n)-time algorithms for patterns of height 1. We also prove that if the height and number of colors in the pattern is fixed, the non-uniform variant admits a O(n)-time algorithm while the uniform variant remains NP-complete. The NP-completeness results use a new reduction from a constrained version of a problem on finite state transducers.Comment: An abstract version appears in the proceedings of CIAA 201

One-dimensional staged self-assembly

17th International Conference, DNA 17, Pasadena, CA, USA, September 19-23, 2011. ProceedingsWe introduce the problem of staged self-assembly of one-dimensional nanostructures, which becomes interesting when the elements are labeled (e.g., representing functional units that must be placed at specific locations). In a restricted model in which each operation has a single terminal assembly, we prove that assembling a given string of labels with the fewest stages is equivalent, up to constant factors, to compressing the string to be uniquely derived from the smallest possible context-free grammar (a well-studied O(logn)-approximable problem). Without this restriction, we show that the optimal assembly can be substantially smaller than the optimal context-free grammar, by a factor of Ω √n/log n even for binary strings of length n. Fortunately, we can bound this separation in model power by a quadratic function in the number of distinct glues or tiles allowed in the assembly, which is typically small in practice

Predicate Encryption from Bilinear Maps and One-Sided Probabilistic Rank

In predicate encryption for a function $f$, an authority can create ciphertexts and secret keys which are associated with `attributes\u27. A user with decryption key $K_y$ corresponding to attribute $y$ can decrypt a ciphertext $CT_x$ corresponding to a message $m$ and attribute $x$ if and only if $f(x,y)=0$. Furthermore, the attribute $x$ remains hidden to the user if $f(x,y) \neq 0$. We construct predicate encryption from assumptions on bilinear maps for a large class of new functions, including sparse set disjointness, Hamming distance at most $k$, inner product mod 2, and any function with an efficient Arthur-Merlin communication protocol. Our construction uses a new probabilistic representation of Boolean functions we call `one-sided probabilistic rank,\u27 and combines it with known constructions of inner product encryption in a novel way

Binary pattern tile set synthesis is NP-hard

In the field of algorithmic self-assembly, a long-standing unproven conjecture has been that of the NP-hardness of binary pattern tile set synthesis (2-PATS). The $k$-PATS problem is that of designing a tile assembly system with the smallest number of tile types which will self-assemble an input pattern of $k$ colors. Of both theoretical and practical significance, $k$-PATS has been studied in a series of papers which have shown $k$-PATS to be NP-hard for $k = 60$, $k = 29$, and then $k = 11$. In this paper, we close the fundamental conjecture that 2-PATS is NP-hard, concluding this line of study. While most of our proof relies on standard mathematical proof techniques, one crucial lemma makes use of a computer-assisted proof, which is a relatively novel but increasingly utilized paradigm for deriving proofs for complex mathematical problems. This tool is especially powerful for attacking combinatorial problems, as exemplified by the proof of the four color theorem by Appel and Haken (simplified later by Robertson, Sanders, Seymour, and Thomas) or the recent important advance on the Erd\H{o}s discrepancy problem by Konev and Lisitsa using computer programs. We utilize a massively parallel algorithm and thus turn an otherwise intractable portion of our proof into a program which requires approximately a year of computation time, bringing the use of computer-assisted proofs to a new scale. We fully detail the algorithm employed by our code, and make the code freely available online

Extended formulations from communication protocols in output-efficient time

Deterministic protocols are well-known tools to obtain extended formulations, with many applications to polytopes arising in combinatorial optimization. Although constructive, those tools are not output-efficient, since the time needed to produce the extended formulation also depends on the number of rows of the slack matrix (hence, on the exact description in the original space). We give general sufficient conditions under which those tools can be implemented as to be output-efficient, showing applications to e.g.~Yannakakis' extended formulation for the stable set polytope of perfect graphs, for which, to the best of our knowledge, an efficient construction was previously not known. For specific classes of polytopes, we give also a direct, efficient construction of extended formulations arising from protocols. Finally, we deal with extended formulations coming from unambiguous non-deterministic protocols

Novel modular chimeric antigen receptor spacer for T cells derived from signal regulatory protein alpha Ig-like domains

Background: T cells equipped with chimeric antigen receptors (CAR) have shown remarkable efficacy in targeting B lineage malignancies. Improvement of the CAR structure is needed, however, with a view to developing flexibly modifiable spacers that are inert in interactions with unwanted cells. Specifically, binding to cells carrying receptors for IgG’s crystallizable fragment (FcR), that recognize IgG-derived domains in CARs is to be avoided.Methods: Two novel CARs targeting the CD19 antigen where the IgG1-CH2 and -CH3 domains were replaced with Ig-like domains from signal-regulatory protein α (SIRPα) were designed in silico. An IgG1-based CAR and a CAR lacking both SIRPα and IgG1 domains were used as comparators. The phenotype and memory phenotype of the expanded cells were analyzed by flow cytometry, and CAR T cell activation and cytotoxic efficacy were assessed in co-culture experiments in response to CD19+ target cells. Unwanted interactions with FcR-expressing myeloid cells were interrogated in co-culture assays with THP-1 monocytic cells.Results: T cells carrying the novel SIRPα-based CARs enacted potent in vitro cytotoxicity against CD19 positive B-lineage leukemia cells, comparable to traditional IgG1-based CAR T cells. Co-culture of IgG1-based CAR T cells with FcR-expressing THP-1 monocytic cells led to prominent cell surface expression of CD69 on T cells together with production of Interleukin (IL)-2 and Interferon-γ, and production of IL-1β, indicating activation of the T cells and monocytes, respectively. Longer co-culture led to killing of the monocytes. No signs of T cell nor monocyte activation were detected in co-cultures of SIRPα-based CAR T cells with THP-1 cells. Arming T cells with the SIRPα-based CARs favored differentiation towards CD4+ phenotype during expansion, while the effects on memory phenotype of the T cells were equivalent between the SIRPα- and IgG1-based CARs. In a pilot experiment, T cells modified with one of the SIRPα-based CARs showed dose dependent leukemia cell control.Conclusion: The novel SIRPα based spacers offer a suitable backbone for developing chimeric antigen receptors that evade the off-target binding to FcR while the cells retain a favorable memory phenotype and efficient cytotoxicity, establishing a promising candidate for future in vivo and clinical testing

Distributedly Testing Cycle-Freeness

International audienceWe tackle \emph{local distributed testing} of graph properties. This framework is well suited to contexts in which data dispersed among the nodes of a network can be collected by some central authority (like in, e.g., sensor networks). In local distributed testing, each node can provide the central authority with just a few information about what it perceives from its neighboring environment, and, based on the collected information, the central authority is aiming at deciding whether or not the network satisfies some property. We analyze in depth the prominent example of checking \emph{cycle-freeness}, and establish tight bounds on the amount of information to be transferred by each node to the central authority for deciding cycle-freeness. In particular, we show that distributedly testing cycle-freeness requires at least $\lceil{\log d}\rceil-1$ bits of information per node in graphs with maximum degree~$d$, even for connected graphs. Our proof is based on a novel version of the seminal result by Naor and Stockmeyer (1995) enabling to reduce the study of certain kinds of algorithms to order-invariant algorithms, and on an appropriate use of the known fact that every free group can be linearly ordered

On the Streaming Indistinguishability of a Random Permutation and a Random Function

An adversary with $S$ bits of memory obtains a stream of $Q$ elements that are uniformly drawn from the set $\{1,2,\ldots,N\}$, either with or without replacement. This corresponds to sampling $Q$ elements using either a random function or a random permutation. The adversary\u27s goal is to distinguish between these two cases. This problem was first considered by Jaeger and Tessaro (EUROCRYPT 2019), which proved that the adversary\u27s advantage is upper bounded by $\sqrt{Q \cdot S/N}$. Jaeger and Tessaro used this bound as a streaming switching lemma which allowed proving that known time-memory tradeoff attacks on several modes of operation (such as counter-mode) are optimal up to a factor of $O(\log N)$ if $Q \cdot S \approx N$. However, the bound\u27s proof assumed an unproven combinatorial conjecture. Moreover, if $Q \cdot S \ll N$ there is a gap between the upper bound of $\sqrt{Q \cdot S/N}$ and the $Q \cdot S/N$ advantage obtained by known attacks. In this paper, we prove a tight upper bound (up to poly-logarithmic factors) of $O(\log Q \cdot Q \cdot S/N)$ on the adversary\u27s advantage in the streaming distinguishing problem. The proof does not require a conjecture and is based on a hybrid argument that gives rise to a reduction from the unique-disjointness communication complexity problem to streaming

Lower bounds for unambiguous automata via communication complexity

We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results. 1. Complement: There is a language L recognised by an n-state UFA such that the complement language L requires NFAs with n Ω(log ˜ n) states. This improves on a lower bound by Raskin. 2. Union: There are languages L1, L2 recognised by n-state UFAs such that the union L1 ∪ L2 requires UFAs with n Ω(log ˜ n) states. 3. Separation: There is a language L such that both L and L are recognised by n-state NFAs but such that L requires UFAs with n Ω(log n) states. This refutes a conjecture by Colcombet