We consider the two-party quantum communication complexity of the bit version of the pointer chasing problem, originally studied by Klauck, Nayak, Ta-Shma and Zuckerman [KNTZ01]. We show that in any quantum protocol for this problem, the two players must exchange Ω( n k4 ) qubits. This improves the previous best bound of Ω( n 22 O(k) ) in [KNTZ01], and comes significantly closer to the best upp...

Oestrogenic steroid hormones (‘oestrogens’) have a crucial role in cellular regulation in all vertebrate species. The levels required to bring about such changes are very low, around 0.1–1 pg/ml (picograms per millilitre) of serum. It has been known for over five decades that oestrogens affect the development of the male reproductive system of mammals (Zuckerman, 1940). Nonetheless, oestrogenic...

Gopalan, Klivans, and Zuckerman proposed a list-decoding algorithm for Reed-Muller codes. Their algorithm works up to a given list-decoding radius. Dumer, Kabatiansky, and Tavernier improved the complexity of the algorithm for binary Reed-Muller codes by using wellknown Plotkin construction. In this study, we propose a list-decoding algorithm for non-binary Reed-Muller codes as a natural genera...

Harmonic Maass forms have recently been related to many different topics in number theory: Ramanujan’s mock theta functions, Dyson’s rank generating functions, Borcherds products, and central values and derivatives of quadratic twists of modular L-functions. Motivated by these connections, we obtain exact formulas for the coefficients of harmonic Maass forms of non-positive weight, and we obtai...

Extractors are boolean functions that allow, in some precise sense, extraction o f randomness from somewhat random distributions. Extractors, and the closely related “Dispersers”, exhibit some of the most “random-like” properties of explicitly constructed combinatorial structures. In turn, extractors and dispersers have many applications in “removing randomness” in various settings, and in maki...

We obtain the first deterministic randomness extractors for n-bit sources with minentropy ≥ n1−α generated (or sampled) by single-tape Turing machines running in time n2−16α, for all sufficiently small α > 0. We also show that such machines cannot sample a uniform n-bit input to the Inner Product function together with the output. The proofs combine a variant of the crossing-sequence technique ...

The BRST cohomology analysis of Lian and Zuckerman leads to physical states at all ghost number for c < 1 matter coupled to Liouville gravity. We show how these states are related to states at ghost numbers zero(pure vertex operator states – DK states) and ghost number one(ring elements) by means of descent equations. These descent equations follow from the double cohomology of the String BRST ...

It is well-known that the standard no-ghost theorem can be extended to the general c = 26 CFT with d-dimensional Minkowski spacetime M(1,d−1) and a compact unitary CFT K of central charge cK = 26 − d. The theorem has been established under the assumption d ≥ 2 so far. We prove the no-ghost theorem for d = 1, i.e., when only the timelike direction is flat. This is done using the technique of Fre...

We provide another proof of the Sipser–Lautemann Theorem by which BPP ⊆ MA (⊆ PH). The current proof is based on strong results regarding the amplification of BPP, due to Zuckerman (1996). Given these results, the current proof is even simpler than previous ones. Furthermore, extending the proof leads to two results regarding MA: MA ⊆ ZPP (which seems to be new), and that two-sided error MA equ...

The 82nd general meeting of the Association of Clinical Pathologists was held in Harrogate on 17, 18, and 19 April 1969. The programme included a symposium on 'The small intestine' at which invited speakers read the papers. This symposium will be published in the Journal later in the year. The second symposium was concerned with 'Radioisotopes in the pathology laboratory'. There was also a foru...