Algorithmic Information Theory and Foundations of Probability

The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed

Using secret sharing for searching in encrypted data

When outsourcing data to an untrusted database server, the data should be encrypted. When using thin clients or low-bandwidth networks it is best to perform most of the work at the server. We present a method, inspired by secure multi-party computation, to search efficiently in encrypted data. XML elements are translated to polynomials. A polynomial is split into two parts: a random polynomial for the client and the difference between the original polynomial and the client polynomial for the server. Since the client polynomials are generated by a random sequence generator only the seed has to be stored on the client. In a combined effort of both the server and the client a query can be evaluated without traversing the whole tree and without the server learning anything about the data or the query

Neutron starquakes and the nature of gamma-ray bursts

The possibility that gamma-ray bursts originate from quakes deep in the solid crust of a neutron star is investigated. Seismic waves are radiated if shear stress is relieved by brittle fracture. However they cannot propagate directly to the surface but are temporarily trapped below a reflecting layer. The shaking of the stellar surface couples the seismic waves to Alfven waves which propagate out into the magnetosphere. The crust-magnetosphere transmission coefficient strongly increases with wave frequency and magnetic field strength. Alfven wave luminosities sufficient to power galactic gamma-ray bursts are possible if magnetic fields greater than 100 billion G cover at least part of the stellar surface. As the Alfven waves propagate out into the low density magnetosphere, they become increasingly charge starved, thereby accelerating particles to relativistic energies

Predictable arguments of knowledge

We initiate a formal investigation on the power of predictability for argument of knowledge systems for NP. Specifically, we consider private-coin argument systems where the answer of the prover can be predicted, given the private randomness of the verifier; we call such protocols Predictable Arguments of Knowledge (PAoK). Our study encompasses a full characterization of PAoK, showing that such arguments can be made extremely laconic, with the prover sending a single bit, and assumed to have only one round (i.e., two messages) of communication without loss of generality. We additionally explore PAoK satisfying additional properties (including zero-knowledge and the possibility of re-using the same challenge across multiple executions with the prover), present several constructions of PAoK relying on different cryptographic tools, and discuss applications to cryptography

Testing formula satisfaction

We study the query complexity of testing for properties defined by read once formulae, as instances of massively parametrized properties, and prove several testability and non-testability results. First we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries exponential in \epsilon and independent of all other parameters. When the gates are limited to being monotone, we prove that there is an estimation algorithm, that outputs an approximation of the distance of the input from satisfying the property. For formulae only involving And/Or gates, we provide a more efficient test whose query complexity is only quasi-polynomial in \epsilon. On the other hand we show that such testability results do not hold in general for formulae over non-Boolean alphabets; specifically we construct a property defined by a read-once arity 2 (non-Boolean) formula over alphabets of size 4, such that any 1/4-test for it requires a number of queries depending on the formula size

The Range of Topological Effects on Communication

We continue the study of communication cost of computing functions when inputs are distributed among $k$ processors, each of which is located at one vertex of a network/graph called a terminal. Every other node of the network also has a processor, with no input. The communication is point-to-point and the cost is the total number of bits exchanged by the protocol, in the worst case, on all edges. Chattopadhyay, Radhakrishnan and Rudra (FOCS'14) recently initiated a study of the effect of topology of the network on the total communication cost using tools from $L_1$ embeddings. Their techniques provided tight bounds for simple functions like Element-Distinctness (ED), which depend on the 1-median of the graph. This work addresses two other kinds of natural functions. We show that for a large class of natural functions like Set-Disjointness the communication cost is essentially $n$ times the cost of the optimal Steiner tree connecting the terminals. Further, we show for natural composed functions like $\text{ED} \circ \text{XOR}$ and $\text{XOR} \circ \text{ED}$, the naive protocols suggested by their definition is optimal for general networks. Interestingly, the bounds for these functions depend on more involved topological parameters that are a combination of Steiner tree and 1-median costs. To obtain our results, we use some new tools in addition to ones used in Chattopadhyay et. al. These include (i) viewing the communication constraints via a linear program; (ii) using tools from the theory of tree embeddings to prove topology sensitive direct sum results that handle the case of composed functions and (iii) representing the communication constraints of certain problems as a family of collection of multiway cuts, where each multiway cut simulates the hardness of computing the function on the star topology

Cost implication analysis of concrete and Masonry waste in construction project

Concrete and masonry waste are the main types of waste typically generated at a construction project. There is a lack of studies in the country regarding the cost implication of managing these types of construction waste To address this need in Malaysia, the study is carried out to measure the disposal cost of concrete and masonry waste. The study was carried out by a site visit method using an indirect measurement approach to quantify the quantity of waste generated at the project. Based on the recorded number of trips for waste collection, the total expenditure to dispose the waste were derived in three construction stages. Data was collected four times a week for the period July 2014 to July 2015. The total waste generated at the study site was 762.51 m3 and the cost incurred for the 187 truck trips required to dispose the waste generated from the project site to the nearby landfill was RM22,440.00. The findings will be useful to both researchers and policy makers concerned with construction waste

Testing Cluster Structure of Graphs

We study the problem of recognizing the cluster structure of a graph in the framework of property testing in the bounded degree model. Given a parameter $\varepsilon$, a $d$-bounded degree graph is defined to be $(k, \phi)$-clusterable, if it can be partitioned into no more than $k$ parts, such that the (inner) conductance of the induced subgraph on each part is at least $\phi$ and the (outer) conductance of each part is at most $c_{d,k}\varepsilon^4\phi^2$, where $c_{d,k}$ depends only on $d,k$. Our main result is a sublinear algorithm with the running time $\widetilde{O}(\sqrt{n}\cdot\mathrm{poly}(\phi,k,1/\varepsilon))$ that takes as input a graph with maximum degree bounded by $d$, parameters $k$, $\phi$, $\varepsilon$, and with probability at least $\frac23$, accepts the graph if it is $(k,\phi)$-clusterable and rejects the graph if it is $\varepsilon$-far from $(k, \phi^*)$-clusterable for $\phi^* = c'_{d,k}\frac{\phi^2 \varepsilon^4}{\log n}$, where $c'_{d,k}$ depends only on $d,k$. By the lower bound of $\Omega(\sqrt{n})$ on the number of queries needed for testing graph expansion, which corresponds to $k=1$ in our problem, our algorithm is asymptotically optimal up to polylogarithmic factors.Comment: Full version of STOC 201

Lunar and planetary studies

This grant supports the core program in planetary astronomy at Caltech. The research includes observations in the IR, sub-mm, mm and cm wavelengths at national and Caltech observatories with a strong emphasis on integrating the observations with spacecraft data and with models of atmospheric structure, dynamics and chemistry. Muhleman's group made extensive observations of Saturn, Uranus and Neptune which are being interpreted in terms of deep atmospheric structures which are obvious in the 2 and 6 cm maps of Saturn and Uranus. The microwave measurements are one of the few sources of information below the 2 bar level. Goldreich is investigating the dynamics of narrow rings with postdoctoral fellow, Pierre-Yves Longaretti. Their work has focused on the role of collisional stresses on the precession of the rings, since the Voyager radio science results imply that the previous model based on the ring's self-gravity is not the entire story. In addition Borderies, Goldreich and Tremaine have completed an investigation of the dynamics of the Encke division in Saturn's A ring

The Melbourne Shuffle: Improving Oblivious Storage in the Cloud

We present a simple, efficient, and secure data-oblivious randomized shuffle algorithm. This is the first secure data-oblivious shuffle that is not based on sorting. Our method can be used to improve previous oblivious storage solutions for network-based outsourcing of data