Related papers: Solution to the Counterfeit Coin Problem and its G…
Multi-class classification is mandatory for real world problems and one of promising techniques for multi-class classification is Error Correcting Output Code. We propose a method for constructing the Error Correcting Output Code to obtain…
The counterfeit goods trade represents nowadays more than 3.3% of the whole world trade and thus it's a problem that needs now more than ever a lot of attention and a reliable solution that would reduce the negative impact it has over the…
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…
In this paper, we study the subset-sum problem by using a quantum heuristic approach similar to the verification circuit of quantum Arthur-Merlin games. Under described certain assumptions, we show that the exact solution of the subset sum…
We generalize the well-known Coupon Collector Problem (CCP) in combinatorics. Our problem is to find the minimum and expected number of draws, with replacement, required to recover $n$ distinctly labeled coupons, with each draw consisting…
We find out the number of different partitions of an n-kilogram stone into the minimum number of parts so that all integral weights from 1 to n kilograms can be weighed in one weighing using the parts of any of the partitions on a two-pan…
Counterfeiting and piracy are a form of theft that has been steadily growing in recent years. Banknotes and identity documents are two common objects of counterfeiting. Aiming to detect these counterfeits, the present survey covers a wide…
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
Deepfake detection remains a challenging task due to the difficulty of generalizing to new types of forgeries. This problem primarily stems from the overfitting of existing detection methods to forgery-irrelevant features and…
We consider a generalisation of the classical coupon collector's problem, in which at each time step a collector either receives a new copy of a randomly chosen coupon, or loses all their previously collected copies of that coupon. We…
We consider a somehow peculiar Token/Bucket problem which at first sight looks confusing and difficult to solve. The winning approach to solve the problem consists in going back to the simple and traditional methods to solve computer…
A new variant of the Compressed Sensing problem is investigated when the number of measurements corrupted by errors is upper bounded by some value l but there are no more restrictions on errors. We prove that in this case it is enough to…
We present a formulation of the problem of finding the smallest T -Count circuit that implements a given unitary as a binary search over a sequence of continuous minimization problems, and demonstrate that these problems are numerically…
Affine quantization is a parallel procedure to canonical quantization, which is ideally suited to deal with special problems. Vector affine quantization introduces multiple degrees of freedom which find that working together create novel…
Forty years ago, Wiesner pointed out that quantum mechanics raises the striking possibility of money that cannot be counterfeited according to the laws of physics. We propose the first quantum money scheme that is (1) public-key, meaning…
The classical Heron problem states: \emph{on a given straight line in the plane, find a point $C$ such that the sum of the distances from $C$ to the given points $A$ and $B$ is minimal}. This problem can be solved using standard geometry or…
Quantum counting is the task of determining the dimension of the subspace of states that are accepted by a quantum verifier circuit. It is the quantum analog of counting the number of valid solutions to NP problems -- a problem well-studied…
Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make…
A problem faced by many instructors is that of designing exams that accurately assess the abilities of the students. Typically these exams are prepared several days in advance, and generic question scores are used based on rough…
This article proposes a novel algorithm for solving mismatch problem in compressed sensing. Its core is to transform mismatch problem into matched by constructing a new measurement matrix to match measurement value under unknown measurement…