In this work, we search for signatures of gravitational millilensing in gamma-ray bursts (GRBs) in which the source−lens−observer geometry produces two images that manifest in the GRB light curve as superimposed peaks with identical temporal variability (or echoes), separated by the time delay between the two images. According to the sensitivity of our detection method, we consider millilensing events due to point-mass lenses in the range of 105 − 107 M ⊙ at lens redshift about half that of the GRB, with a time delay on the order of 10 s. Current GRB observatories are capable of resolving and constraining this lensing scenario if the above conditions are met. We investigated the Fermi/GBM GRB archive from the year 2008 to 2020 using the autocorrelation technique and found one millilensed GRB candidate out of 2137 GRBs searched, which we use to estimate the optical depth of millilensed GRBs by performing a Monte Carlo simulation to find the efficiency of our detection method. Considering a point-mass model for the gravitational lens, where the lens is a supermassive black hole, we show that the density parameter of black holes (ΩBH) with mass ≈ 106 M ⊙ is about 0.007 ± 0.004. Our result is one order of magnitude larger compared to previous work in the lower mass range of 102 − 103 M ⊙, which gave a density parameter ΩBH ≈ 5 × 10−4, and recent work in the mass range of 102 − 107 M ⊙, which reported ΩBH ≈ 4.6 × 10−4. The mass fraction of black holes in this mass range to the total mass of the universe would be f = ΩBH/Ω M ≈ 0.027 ± 0.016.

Gravitational lensing of gamma-ray bursts (GRBs) can provide an opportunity to probe the massive compact objects in the universe at different redshifts. We have discovered two consecutive pulses in the light curve of GRB 090717034, with the same temporal profile and different count rate, separated by a time interval, which is identified as a gravitationally lensed candidate in the Fermi-GBM GRB catalog. Here, we use the χ 2 minimization method to investigate the similarity of the temporal profile variability of the two pulses as a gravitationally lensed GRB candidate. We find the magnification factor and the time delay between two pulses to minimize the χ 2 function. Then, we perform a Monte Carlo simulation on a sample of mock lensed GRBs and compare the χ 2 of the lensed GRB candidate with the simulation, which confirms this candidate with 1σ confidence level. Assuming that GRB 090717034 is lensed by a pointlike object, the redshifted lens mass is about M L (1 + z) = (4.839 ± 1.148) × 106 M ⊙. The lens of this GRB is a candidate for a supermassive black hole along the line of sight to the GRB.

Reversible logic has been emerged as a promising computing paradigm to design low power circuits in recent years. The synthesis of reversible circuits is very different from that of non-reversible circuits. Many researchers are studying methods for synthesizing reversible combinational logic. Some automated reversible logic synthesis methods use optimization algorithms Optimization algorithms are used in some automated reversible logic synthesis techniques. In these methods, the process of finding a circuit for a given function is a very time-consuming task, so it"s better to design a processor which speeds up the process of synthesis. Application specific instruction set processors (ASIP) can benefit the advantages of both custom ASIC chips and general DSP chips. In this paper, a new architecture for automatic reversible logic synthesis based on an Application Specific Instruction set Processors is presented. The essential purpose of the design was to provide the programmability with the specific necessary instructions for automated synthesis reversible. Our proposed processor that we referred to as ARASP is a 16-bit processor with a total of 47 instructions, which some specific instruction has been set for automated synthesis reversible circuits. ARASP is specialized for automated synthesis of reversible circuits using Genetic optimization algorithms. All major components of the design are comprehensively discussed within the processor core. The set of instructions is provided in the Register Transform Language completely. Afterward, the VHDL code is used to test the proposed architecture.